^ 


19 


ToFTrtE 

tmiVEB$ITY 
OF 


University  of  California  •  Berkeley 


1 


CONVERSATIONS 


THE  ELEMENTS   OF   THAT   SCIENCE 

ARE 

FAMILIARLY  EXPLAINED, 

AND  ADAPTED  TO  THE 

COMPREHENSION   OF   YOUNG    PUPILS. 


3(nu0trateii  iDttti  piate^. 


BY  THE  AUTHOR  OF  CONVERSATIONS  ON  CHEMISTRV, 

AND  CONVERSATIONS  ON  POLITICAL 

ECONOMY. 


NEW-YORK  : 

PUBLISHED  BY  A.  T.  GOODRICH,  W.  B.  GILLEY,  AND  CHARLES 
WILEY  k  CO. 

Clayton  fy  Kingdand,  Printers. 

1820. 


^-^•- 


A 


5^^:  V 


recommendation/ 


The  very  pleasing  style  in  which  the  Conver- 
sations on  Chemistry  were  written^  and  the  re- 
markable clearness  with  which  they  illustrated 
the  leading  facts  6/  that  science^  have  undqnbt- 
edly  contributed  to  render  the  study  of  it  more 
popular.  The  same  observation  applies  to  the 
Conversations  on  Political  Economy — a  'subr- 
ject  so  obscure  as  to  have  been  considered  as 
fit  only  for  philosophers  and  statesmen  has  been 
brought  to  the  level  of  common  understandings^ 
and  devested  of  all  its  repulsive  features.  Upon 
looking  hastily  into  the  present  volume^  it  ap- 
pears to  me  to  be  distinguished  by  the  same 
clearness  of  elucidation  as  the  former  produc- 
tions of  the  amiable  author;  and  it  will^  I  have 
no  doubt^  prove  to  be  a  valuable  addition  to  the 
popular  works  on  natural  philosophy, 

J.  GRISCOM. 

New-York,  llth  month  24th,  1819. 


■is^y 


*?«:> 


PREFACE, 


It  is  with  increased  diffidence  that  the 
author  offers  this  little  work  to  the  public. 
The  encouraging  reception  which  the 
Conversations  on  Chemistry  and  Political 
Economy  have  met  with,  has  induced  her 
to  venture  on  publishing  a  short  course  on 
Natural  Philosophy ;  but  not  without  the 
greatest  apprehensions  for  its  success. 
Her  ignorance  of  mathematics,  and  the 
imperfect  knowledge  of  natural  philoso- 
phy which  that  disadvantage  necessarily 
implies,  renders  her  fully  sensible  of  her 
incompetency  to  treat  the  subject  in  any 
other  way  than  in  the  form  of  a  familiar 
explanation  of  the  first  elements,  for  the 
use  of  very  young  pupils.  It  is  the  hope 
of  having  done  this  in  a  manner  that  may 
engage  their  attention,  which  encourages 

her  to  offer  them  these  additional  lessons, 
1* 


VI  PREFACE. 

They  are  intended,  in  a  course  of  ele- 
mentary science,  to  precede  the  Conver- 
sations on  Chemistry;  and  were  actually 
written  previous  to  either  of  her  former 
publications. 


CONTENTS. 


CONVERSATION  I. 

ON  GENERAL  PROPERTIES  OF  BODIES. 

Introduction — General  Properties  of  Bodies — Impenetrability  > 
Extension — Figure — Divisibility — Inertia — Attraction — At- 
traction of  Cohesion — Density — Rarity — Heat — Attraction  of 
Gravitation,  13 

CONVERSATION  II. 

ON  THE  ATTRACTION  OF  GRAVITY. 

Attraction  of  Gravitation,  continued — Of  Weight — Of  the  Fall 
of  Bodies — Of  the  Resistance  of  the  Air — Of  the  Ascent  of 
Light  Bodies,  •         29 

CONVERSATION  III. 

ON  THE  LAWS  OF  MOTION. 

Of  Motion — Of  the  Inertia  of  Bodies — Of  Force  to  Produce 
Motion — Direction  of  Motion — Velocity,  absolute  and  rela- 
tive— Uniform  Motion — Retarded  Motion — Accelerated  iVIo- 
tion — Velocity  of  Falling  Bodies — Momentum — Action  and 
Reaction  Equal — Elasticity  of  Bodies — Porosity  of  Bodies — 
Reflected  Motion — Angles  of  Incidence  and  Reflection,     43 

CONVERSATION  IV. 

ON  COMPOUND  MOTION. 

Compound  Motion,  the  result  of  two  opposite  forces — Of  Circu- 
lar Motion,  the  result  of  two  forces,  one  of  which  confines 
the  body  to  a  fixed  point — Centre  of  Motion,  the  point  at  rest 
while  the  other  parts  of  the  body  move  round  it — Centre  of 
Magnitude,  the  middle  of  a  body — Centripetal  Force,  that 


Vlll  CONTENTS. 

which  confines  a  body  to  a  fixed  central  point — Centrifugal 
Force,  that  which  impels  a  body  to  fly  from  the  centre — Fall 
of  Bodies  in  a  Parabola — Centre  of  Gravity,  the  Centre  of 
Weight,  or  point  about  which  the  parts  balance  each  other,  59 

CONVERSATION  V. 

ON  THE  MECHANICAL  POWERS. 

Of  the  Power  of  Machines — Of  the  Lever  in  General' — Of  the 
Lever  of  the  first  kind,  having  the  Fulcrum  between  the 
Power  and  the  Weight — Of  the  Lever  of  the  second  kind, 
having  the  Weight  between  the  Power  and  the  Fulcrum — Of 
the  Lever  of  the  third  kind,  having  the  Power  between  the 
Fulcrum  and  the  Weight— Of  the  Pulley— Of  the  Wheel  and 
Axle— Of  the  Inclined  Plane — Of  the  Wedge— of  the  Screw, 

79 

CONVERSATION  VI. 

ASTRONOMy. 
CAUSES  OF  THE  EARTH's  ANNUAL  MOTION. 

Of  the  Planets,  and  their  Motion — Of  the  Diurnal  Motion  of 
the  Earth  and  Planets,  90 

CONVERSATION  VII. 

ON  THE  PLANETS. 

Of  the  Satellites  or  Moons — Gravity  Diminishes  as  the  Square 
of  the  Distance— Of  the  Solar  System — Of  Comets— Constel- 
lations, signs  of  the  Zodiac — Of  Copernicus,  Newton,  kc.  102 

CONVERSATION  VIII. 

ON  THE  EARTH. 

Of  the  Terrestrial  Globe— Of  the  Figure  of  the  Earth— Of  the 
Pendulum— Of  the  Variation  of  the  Seasons,  and  of  the 
Length  of  Days  and  Nights — Of  the  Causes  of  the  Heat  of 
Summer— Of  Solar,  Sidereal,  aad  Equal  or  Mean  Time,  114 


CONTENTS.  iX 

CONVERSATION  IX 

ON  THE  MOON. 

Of  the  Moon's  Motion — Phases  of  the  Moon — Eclipses  of  the 
Moon — Eclipses  of  Jupiter's  Moons — Of  the  Latitude  and 
Longitude — Of  the  Transits  of  the  Inferior  Planets — Of  the 
Tides,  134 

CONVERSATION  X. 

HYDROSTATICS. 
ON  THE  MECHANICAL  PROPERTIES  OF  FLUIDS. 

Definition  of  a  Fluid — Distinction  between  Fluids  and  Liquids 
— Of  Non-Elastic  Fluids,  scarcely  susceptible  of  Compression 
— Of  the  Cohesion  of  Fluids — Of  their  Gravitation — Of  their 
Equilibrium—Of  their  Pressure — Of  Specific  Gravity — Of  the 
Specific  Gravity  of  Bodies  heavier  than  Water — Of  those  of 
the  same  weight  as  Water — Of  those  lighter  than  Water — Of 
the  Specific  Gravity  of  Fluids,  146 

CONVERSATION  XI. 

OF  SPRINGS,  FOUNTAINS,  k,C. 

Of  the  Ascent  of  Vapour  and  the  Formation  of  Clouds — Of  the 
Formation  and  Fall  of  Rain,  &,c. — Of  the  Formation  of 
Springs — Of  Rivers  and  Lakes — Of  Fountains,  159 

CONVERSATION  XII. 

PNEUMATICS. 
ON  THE  MECHANICAL  PROPERTIES  OF  AIR. 

Of  the  Spring  or  Elasticity  of  the  Air— Of  the  Weight  of  the  Air 
— Experiments  with  the  Air  Pump — Of  the  Barometer — Mode 
of  Weighing  Air — Specific  Gravity  of  Air — Of  Pumps — De- 
scription of  the  Sucking  Pump— Description  of  the  Forcing 
Pump,  168 


X  CONTEWrS.. 

eONVERSATION  XIII. 

ON  WIND  AND  SOUND. 

Of  Wind  in  General— Of  the  Trade  Wind— Of  the  Periodica 
Trade  Winds— Of  the  Aerial  Tides— Of  Sound  in  General— 
Of  Sonorous  Bodies— Of  Musical  Sounds— Of  Concord  or 
Harmony,  and  Melody,  '  180 

CONVERSATION  XIV. 

ON  OPTICS. 

Of  Luminous,  Transparent,  and  Opaque  Bodies— Of  the  Radia- 
tion of  Light — Of  Shadows — Of  the  Reflection  of  Light — 
Opaque  Bodies  seen  only  by  Reflected  Light — Vision  Ex- 
plained— Camera  Obscura — Image  of  Objects  on  the  Retina, 

194 

CONVERSATION  XV. 

ON  THE  ANGLE  OF  VISION,  AND  THE  REFLECTION  OF  MIRRORS. 

Angle  of  Vision — Reflection  of  Plain  Mirrors — Reflection  of 
Convex  Mirrors — Reflection  of  Concave  Mirrors,  208 

CONVERSATION  XVF. 

ON  REFRACTION  AND  COLOURS. 

Transmission  of  Light  by  Transparent  Bodies — Refraction — 
Refraction  of  the  Atmosphere — Refraction  of  a  Lens — Re- 
fraction of  the  Prism— Of  the  Colours  of  Rays  of  Light— Of 
the  Colours  of  Bodies,  223 

CONVERSATION  XVII. 

OPTICS. 
O^  THE  STRUCTURE  OF  THE  EYE,  AND  OPTICAL  INSTRUMENTS. 

Description  of  the  Eye — Of  the  Image  on  the  Retina — Refrac- 
tion of  the  Humours  of  the  Eye — Of  the  Use  of  Spectacles — 
Of  the  Single  Microscope — Of  the  Double  Microscope — Of 
the  Solar  Microscope — Magic  Lauthorn — Refracting  Tele- 
scope— Reflecting  Telescope,  241 


DIRECTIONS 

FOR  PLACING  THE  ENGRAVINGS. 


late  I.  to  face  page  34 

II. 

-     66 

III. 

62 

IV. 

-     70 

V. 

79 

VI. 

-         -     91 

VII. 

-       104 

VIII. 

-  108 

IX. 

-       116 

X. 

-    •      -  128 

XI. 

-       132 

XII. 

-  136 

XIII. 

-       148 

XIV. 

-  164 

XV. 

-       195 

XVI. 

-  203 

XVII. 

-       208 

XVIII. 

.  217 

XIX. 

.       224 

XX. 

-  228 

XXI. 

-       241 

XXII. 

-         .246 

XXIII. 

-       249 

ERRATUM. 
Page  62,  for  Plate  III.  read  Plate  IV. 


CONVERSATION  I. 


ON  GENERAL  PROPERTIES  OF  BODIES. 

Introduction. —  General  Properties  of  Bodies. — Impe- 
netrability.— Extension. Figure. Divisibility. — 

Inertia. — .Attraction. — Attraction  of  Cohesion. — Den- 
sity.— Rarity. — Heat. — Attraction  of  Gravitation. 

EjMILY.  I  must  request  your  assistance,  my  dear 
Mrs.  B.,  in  a  charge  which  I  have  lately  undertaken : 
it  is  that  of  instructing  my  youngest  sister,  a  task, 
whicli  I  find  proves  more  difficult  than  I  had  at  first 
imagined.  I  can  teach  her  the  common  routine  of 
children's  lessons  tolerably  well ;  but  she  is  such  an 
inquisitive  little  creature,  that  she  is  not  satisfied 
without  an  explanation  of  every  difficulty  that  occurs 
to  her,  and  frequently  asks  me  questions  which  I  am 
at  a  loss  to  answer.  This  morning,  for  instance, 
when  I  had  explained  to  her  that  the  world  was 
round  like  a  ball,  instead  of  being  flat  as  she  had  sup- 
posed, and  that  it  was  surrounded  by  the  air,  she  ask- 
ed me  what  supported  it.  I  told  her  that  it  required 
no  support ;  she  then  inquired  why  it  did  not  fall  as 
every  thing  else  did  ?  This  I  confess  perplexed  me  ; 
for  I  had  myself  been  satisfied  with  learning  that  the 
world  floated  in  the  air,  without  considering  how  un- 
natural it  was  that  so  heavy  a  body,  bearing  the  weight 
of  all  other  things,  should  be  able  to  support  itself. 

Mrs.  B.  1  make  no  doubt,  my  dear,  but  that  1  shall 
be  able  to  explain  this  difficulty  to  you  ;  but  I  believe 
that  it  would  be  almost  impossible  to  render  it  intelli- 
2 


14  GENERAL  PROrERTiES  OF  BODIES. 

gible  to  the  comprehension  of  so  young  a  child  as 
your  sister  Sophia.  You,  who  are  now  in  your  thir- 
teenth year,  may,  I  think  with  great  propriety,  learn 
not  only  the  cause  of  this  particular  fact,  but  acquire 
a  general  knowledge  of  the  laws  by  which  the  natural 
world  is  governed. 

Emily.  Of  all  things,  it  is  what  I  should  most  like 
to  learn  ;  but  I  was  afraid  it  was  too  difficult  a  study 
even  at  my  age. 

Mrs.  B.  Not  when  familiarly  explained  :  if  you 
have  patience  to  attend,  I  will  most  willingly  give  you 
all  the  information  in  my  power.  You  may  perhaps 
find  the  subject  rather  dry  at  first ;  but  if  I  succeed 
in  explaining  the  laws  of  nature,  so  as  to  make  you 
understand  them,  I  am  sure  that  you  will  derive  not 
only  instruction,  but  great  amusement  from  that 
study. 

Emily.  I  make  no  doubt  of  it,  Mrs.  B.  ;  and  pray 
begin  by  explaining  why  the  earth  requires  no  sup- 
port ;  for  that  is  the  point  which  just  now  most  strong- 
ly excites  my  curiosity. 

Mrs.  B.  My  dear  Emily,  if  I  am  to  attempt  to  give 
you  a  general  idea  of  the  laws  of  nature,  which  is  no 
less  than  to  introduce  you  to  a  knowledge  of  the  sci- 
ence of  natural  philosophy,  it  will  be  necessary  for  us 
to  proceed  with  some  degree  of  regularity.  I  do  not 
wish  to  confine  you  to  the  systematic  order  of  a  scien- 
tific treatise  ;  but  if  we  were  merely  to  examine  eve- 
ry vague  question  that  may  chance  to  occur,  our  pro- 
gress would  be  but  very  slow.  Let  us,  therefore^ 
begin  by  taking  a  short  survey  of  the  general  proper- 
ties of  bodies,  some  of  which  must  necessarily  be  ex- 
plained before  I  can  attempt  to  make  you  understand 
Tvhy  the  earth  requires  no  support. 

When  I  speak  of  bodies,  I  mean  substances,  of  what- 
ever nature,  whether  solid  or  fluid  ;  and  matter  is  the 
general  term  used  to  denote  the  substance,  whatever 
its  nature  be,  of  which  the  different  bodies  are  com- 
posed.    Thus,  wood  is  tliQ  matter  of  which  this  table 


GENERAL  PROPERTIES  OF  BODIES.       lb 

IS  made  ;  water  is  the  matter  with  which  this  glass  is 
tilled,  &c- 

Emily.  I  am  very  glad  you  have  explained  the 
meaning  of  the  word  matter,  as  it  has  corrected  an  er- 
roneous conception  I  had  formed  of  it :  I  thought  that 
it  was  applicable  to  solid  bodies  only. 

Mrs.  B.  There  are  certain  properties  which  ap- 
pear to  be  common  to  all  bodies,  and  are  hence  called 
the  essential  properties  of  bodies ;  these  are,  Impene- 
(rability,  Extension,  Figure,  Divisibility,  Inertia,  and 
Attraction.  These  arc  called  the  general  properties 
of  bodies,  as  we  do  not  suppose  any  body  to  exist  with- 
out them. 

By  impenetrability,  is  meant  the  property  which 
bodies  have  of  occupying  a  certain  space,  so  that, 
where  one  body  is,  another  cannot  be,  without  dis- 
placing the  former ;  for  tvvo  bodies  cannot  exist  in  the 
same  place  at  the  same  time.  A  liquid  may  be  more 
easily  removed  than  a  solid  body ;  yet  it  is  not  the 
less  substantial,  since  it  is  as  impossible  for  a  liquid 
and  a  solid  to  occupy  the  same  space  at  the  same  time, 
as  for  two  solid  bodies  to  do  so.  For  instance,  if  you 
put  a  spoon  into  a  glass  full  of  water,  the  water  will 
flow  over  to  make  room  for  the  spoon. 

Emily.  1  understand  this  perfectly.  Liquids  are 
in  reality  as  substantial  or  as  impenetrable  as  solid 
bodies,  and  they  appear  less  so,  only  because  they 
are  more  easily  displaced. 

Mrs.  B.  The  air  is  a  fluid  differing  in  its  nature 
from  liquids,  but  no  less  impenetrable.  If  I  endea- 
vour to  till  this  phial  by  plunging  it  into  this  basin  of 
water,  the  air,  you  see,  rushes  out  of  the  phial  in 
bubbles,  in  order  to  make  way  for  the  water,  for  the 
air  and  the  water  cannot  exist  together  in  the  same 
space,  any  more  than  two  hard  bodies  ;  and  if  I  re- 
verse this  goblet,  and  plunge  it  perpendicularly  into 
the  water,  so  that  the  air  will  not  be  able  to  escape, 
the  water  will  no  longer  be  able  to  till  the  goblet. 

Emily,  But  it  rises  a  considerable  way  into  the 
glass. 


16  GENERAL    PROPERTIES  OF  BODIES. 

Mrs.  B.  Because  the  water  compresses  or 
squeezes  the  air  into  a  small  space  in  the  upper  part 
of  the  glass  .  but,  as  long  as  it  remains  there,  no 
other  body  can  occupy  the  same  place. 

Emily.  A  difficulty  has  just  occurred  to  me,  with 
regard  to  the  impenetrability  of  solid  bodies  ;  if  a 
nail  is  c!riven  into  a  piece  of  wood,  it  penetrates  it, 
and  both  the  wood  and  the  nail  occupy  the  same  space 
that  the  wood  alone  did  before  ? 

Mrs.  B.  The  nail  penetrates  between  the  parti- 
cles of  the  V  ood,  by  forcing  them  to  make  way  for 
it;  for  you  know  that  not  a  single  atom  of  wood  can 
remain  in  the  space  which  the  nail  occupies ;  and  if 
the  wooo  is  not  increased  in  size  by  the  addition  of  the 
nail,  it  is  because  wood  is  a  porous  substance,  like 
sponge,  the  particles  of  which  may  be  compressed  or 
squeezed  closer  together  ;  and  it  is  thus  that  they 
make  way  for  the  nail. 

We  may  now  proceed  to  the  next  general  property 
(ji  bodies,  extension.  A  body  which  occupies  a  cer- 
tain space  must  necessarily  have  extension  ;  that  is  to 
say,  length,  breadth,  and  depth;  these  are  called  the 
dimensions  of  extension  :  can  you  form  an  idea  of  any 
body  without  them  ? 

Emily.  No  ;  certainly  I  cannot ;  though  these  di- 
mensions must,  of  course,  vary  extremely  in  different 
bodies.  The  length,  breadth,  and  depth  of  a  box,  or 
of  a  tJ.  nble,  are  very  different  from  those  of  a  walk- 
ing-stic'.,  or  of  a  hair. 

But  is  not  height  also  a  dimension  of  extension  ? 

Mrs.  B.  Height  and  depth  are  the  same  dimension, 
considered  in  different  points  of  view  ;  if  you  measure 
a  body,  or  a  space,  from  the  top  to  the  bottom,  you 
call  it  depth ;  if  from  the  bottom  upwards,  you  call  it 
height ;  thus  the  depth  and  height  of  a  box  are,  in 
fact,  the  same  thing. 

Emily.  Very  true ;  a  moment's  consideration 
%vould  have  enabled  me  to  discover  that  ;  and  breadth 
and  width  are  also  the  same  dimension. 

Mrs.  B.     Yes  ;  the  limits  of  extension  constitute 


GENERAL   PROPERTIES  OP  BODIES.  17 

figure  or  shape.  You  conceive  that  a  body  having 
length,  breadth,  and  depth,  cannot  be  without  form, 
either  symmetrical  or  irregular  ? 

Emily.  Undoubtedly  ;  and  this  property  admits  of 
almost  an  infinite  variety. 

Mrs.  B.  Nature  has  assigned  regular  forms  to  her 
productions  in  general.  The  natural  form  of  mineral 
substances  is  that  of  crystals,  of  which  there  is  a  great 
variety.  Many  of  them  are  very  beautiful,  and  no 
less  remarkable  by  their  transparency,  or  colour,  than 
by  the  perfect  regularity  of  their  forms,  as  may  be 
seen  in  the  various  museums  and  collections  of  natu- 
ral history.  The  vegetable  and  animal  creation  ap- 
pears less  symmetrical,  but  is  still  more  diversified  in 
figure  than  the  mineral  kingdom.  Manufactured  sub- 
stances assume  the  various  arbitrary  forms  which  the 
art  of  man  designs  for  them;  and  an  infinite  number 
of  irregular  forms  are  produced  by  fractures,  and  by 
the  dismemberment  of  the  parts  of  bodies. 

Emily.     Such  as  a  piece  of  broken  china,  or  glass  ? 

Mrs.  B.  Or  the  fragments  of  mineral  bodies  which 
are  broken  in  being  dug  out  of  the  earth,  or  decayed 
by  the  effect  of  torrents  and  other  causes.  The  pic- 
turesque effect  of  rock-scenery  is  in  a  great  measure 
owing  to  accidental  irregularities  of  this  kind. 

We  may  now  proceed  to  divisibility  ;  that  is  to  say, 
a  susceptibility  of  being  divided  into  an  indefinite  num- 
ber of  parts.  Take  any  small  quantity  of  matter,  a 
grain  of  sand  for  instance,  and  cut  it  into  two  parts; 
these  two  parts  might  be  again  divided,  had  we  in- 
struments sufficiently  fine  for  the  purpose  ;  and  if,  by- 
means  of  pounding,  grinding,  and  other  similar  me- 
thods, we  carry  this  division  to  the  greatest  possible 
extent,  and  reduce  the  body  to  its  finest  imaginable 
particles,  yet  not  one  of  the  particles  will  be  destroy- 
ed, and  the  body  will  continue  to  exist,  though  in  this 
altered  state. 

The  melting  of  a  solid  body  in  a  liquid  affords  a  ve- 
ry striking  example  of  the  extreme  divisibility  of  mat- 
ter ;  when  you  sweeten  a  cup  of  tea,  for  instance, 
2* 


18  GENERAL  PROPERTIES  OT  BODTES. 

with  what  minuteness  the  sugar  must  be  divided  to  be 
diffused  throughout  the  whole  of  the  hquid. 

Emily.  And  if  you  pour  a  few  drops  of  red  wine 
into  a  glass  of  water,  they  immediately  tinge  the 
whole  of  the  water,  and  must  therefore  be  diffused 
throughout  it. 

Mrs.  B.  Exactly  so  ;  and  the  perfume  of  this  la- 
vender-water will  be  almost  as  instantaneously  diffu- 
sed throughout  the  room,  if  I  take  out  the  stopper. 

Emily.,  But  in  this  case  it  is  only  the  perfume  of 
the  lavender,  and  not  the  water  itself,  that  is  diffused 
in  the  room  ? 

Mrs.  B.  The  odour  or  smell  of  a  body  is  part  of 
the  body  itself,  and  is  produced  b}'  very  minute  parti- 
cles or  exhalations  which  escape  from  odoriferous  bo- 
dies. It  would  be  impossible  that  you  should  smell 
the  lavender-water,  if  particles  of  it  did  not  come  in 
actual  contact  with  your  nose. 

Emily.  But  when  I  smell  a  flower,  I  see  no  va- 
pour rise  from  it ;  and  yet  I  can  perceive  the  smell 
at  a  considerable  distance. 

Mrs.  B.  You  could,  I  assure  you,  no  more  smell 
a  flower,  the  odoriferous  particles  of  which  did  not 
touch  your  nose,  than  you  could  taste  a  fruit,  the 
flavoured  particles  of  which  did  not  come  in  contact 
with  your  tongue. 

Emily.  That  is  wonderful  indeed;  the  particles 
then,  which  exhale  from  the  flower  and  from  the  la- 
vender-water, are,  I  suppose,  too  small  to  be  visible  ? 

Mrs.  B.  Certainly  :  you  may  form  some  idea  of 
their  extreme  minuteness,  from  the  immense  number 
which  must  have  escaped  in  order  to  perfume  the 
whole  room ;  and  yet  there  is  no  sensible  diminution 
of  the  liquid  in  the  phial. 

Emily.  But  the  quantity  must  really  be  diminish- 
ed? 

Mrs.  B.  Undoubtedly  ;  and  were  you  to  leave 
the  bottle  open  a  sufficient  length  of  time,  the  whole 
of  the  water  would  evaporate  and  disappear.  But 
though  so  minutely  subdivided  as  to  be  imperceptible 


GENERAL  PROPERTIES  OF  BODIES.      19- 

to  any  of  our  senses,  each  particle  would  continue  to 
exist ;  for  it  is  not  within  the  power  of  man  to  de- 
stroy a  single  particle  of  matter ;  nor  is  there  any  rea- 
son to  suppose  that  in  nature  an  atom  is  ever  annihi- 
lated. 

Emily.  Yet,  when  a  body  is  burnt  to  ashes,  part 
of  it,  at  least,  appears  to  be  effectually  destroyed  ? 
Look  how  small  is  the  residue  of  ashes  beneath  the 
grate,  from  all  the  coals  which  have  been  consumed 
within  it. 

Airs.  B.  That  part  of  the  coals,  which  you  sup- 
pose to  be  destroyed,  evaporates  in  the  form  of 
smoke  and  vapour,  whilst  the  remainder  is  reduced 
to  ashes.  A  body,  in  burning,  undergoes  no  doubt 
very  remarkable  changes  ;  it  is  generally  subdivided  ; 
its  form  and  colour  altered  ;  its  extension  increased  : 
but  the  various  parts,  into  which  it  has  been  separa- 
ted by  combustion,  continue  in  existence,  and  retain 
all  the  essential  properties  of  bodies. 

Emily.  But  that  part  of  a  burnt  body  which  eva- 
porates in  smoke  has  no  figure  :  smoke,  it  is  true,  as- 
cends in  columns  into  the  air,  but  it  is  soon  so  much 
diffused  as  to  lose  all  form;  it  becomes  indeed  invisi- 
ble. 

Mrs.  B.  Invisible,  I  allow  ;  but  we  must  not  ima- 
gine that  what  we  no  longer  see  no  longer  exists. 
Were  every  particle  of  matter  that  becomes  invisible 
annihilated,  the  world  itself  would  in  the  course  of 
time  be  destroyed.  The  particles  of  smoke,  when 
difi'used  in  the  air,  continue  still  to  be  particles  of 
matter,  as  well  as  when  more  closely  united  in  the 
form  of  coals:  they  are  really  as  substantial  in  the 
one  state  as  in  the  other,  and  equally  so  when  by 
their  extreme  subdivision  they  become  invisible.  No 
particle  of  matter  is  ever  destroyed  :  this  is  a  princi- 
ple you  must  constantly  remember.  Every  thing  in 
nature  decays  and  corrupts  in  the  lapse  of  time.  We 
die,  and  our  bodies  moulder  to  dust ;  but  not  a  single 
atom  of  them  is  lost ;  they  serve  to  nourish  the  earth, 
whence,  while  living,  they  drew  their  support. 


20  GfiT!?ERAL  PROPERTIES  OF  BODIES. 

The  next  essential  property  of  matter  is  called  in- 
ertia;  this  word  expresses  the  resistance  which  inac- 
tive matter  makes  to  a  change  of  state.  Bodies  ap- 
pear to  be  equally  incapable  of  changing  their  actual 
state,  whether  it  be  of  motion  or  of  rest.  You  know 
that  it  requires  force  to  put  a  body  which  is  at  rest  ia 
motion ;  an  exertion  of  strength  is  also  requisite  to 
stop  a  body  which  is  already  in  motion.  The  resist- 
ance of  the  body  to  a  change  of  state,  in  either  case, 
is  called  its  inertia. 

Emily.  In  playing  at  base-ball  I  am  obliged  to  use 
all  my  strength  to  give  a  rapid  motion  to  the  ball ;  and 
when  I  have  to  catch  it,  I  am  sure  I  feel  the'resistance 
it  makes  to  being  stopped.  But  if  I  did  not  catch  it, 
it  would  soon  fall  to  the  ground  and  stop  of  itself. 

Mrs.  B.  Inert  matter  is  as  incapable  of  stopping  of 
itself,  as  it  is  of  putting  itself  into  motion:  when  the 
ball  ceases  to  move,  therefore,  it  must  be  stopped  by 
some  other  cause  or  power;  but  as  it  is  one  with 
which  you  are  yet  unacquainted,  we  cannot  at  present 
investigate  its  effects. 

The  last  property  which  appears  to  be  common  to 
all  bodies  is  attraction.  All  bodies  consist  of  infinite- 
ly small  particles  of  matter,  each  of  which  possesses 
the  power  of  attracting  or  drawing  towards  it,  and 
uniting  with  any  other  particle  sufficiently  near  to  be 
within  the  influence  of  its  attraction  ;  but  in  minute 
particles  this  power  extends  to  so  very  small  a  dis- 
tance around  them,  that  its  effect  is  not  sensible,  un- 
less they  are  (or  at  least  appear  to  be)  in  contact;  it 
then  makes  them  stick  or  adhere  together,  and  is 
hence  called  the  attraction  of  cohesion.  Without  this 
power,  solid  bodies  would  fall  in  pieces,  or  rather 
crumble  to  atoms. 

Emily.  I  ara  so  much  accustomed  to  see  bodies 
firm  and  solid  that  it  never  occurred  to  me  that  any 
power  was  requisite  to  unite  the  particles  of  which 
they  are  composed.  But  the  attraction  of  cohesion 
does  not,  1  suppose,  exist  in  liquids  ;  for  the  particles 


GENERAL  PROPERTIES  OF  BODIES.  21 

of  liquids  do  not  remain  together  so  as  to  form  a  body, 
unless  confined  in  a  vessel  ? 

Mrs.  B.  I  beg  your  pardon  ;  it  is  the  attraction  of 
cohesion  which  holds  this  drop  of  water  suspended 
at  the  end  of  ray  finger,  and  keeps  the  minute  watery 
particles  of  which  it  is  composed  united.  But  as 
this  power  is  stronger  in  proportion  as  the  particles 
of  bodies  are  more  closely  united,  the  cohesive  at- 
traction of  solid  bodies  is  much  greater  than  that  of 
fluids. 

The  thinner  and  lighter  a  fluid  is,  the  less  is  the  co- 
hesive attraction  of  its  particles,because  they  are  fur- 
ther apart;  and  in  elastic  fluids,  such  as  air,  there  is 
no  cohesive  attraction  among  the  particles. 

Emily.  That  is  very  fortunate  ;  for  it  would  be  im- 
possible to  breathe  the  air  in  a  solid  mass ;  or  even  in 
a  liquid  state. 

But  is  the  air  a  body  of  the  same  nature  as  other 
bodies  ? 

Mrs.  B.     Undoubtedly,  in  all  essential  properties. 

Emily.  Yet  you  say  that  it  does  not  possess  one 
of  the  general  properties  of  bodies — cohesive  attrac- 
tion? 

Mrs.  B.  The  particles  of  air  are  not  destitute  of 
the  power  of  attraction,  but  they  are  too  far  distant 
from  each  other  to  be  influenced  by  it;  and  the  ut- 
most efforts  of  human  art  have  proved  ineff*ectual  in 
the  attempt  to  compress  them,  so  as  to  bring  them 
within  the  sphere  of  each  other's  attraction,  and  make 
them  cohere. 

Emily.  If  so,  how  is  it  possible  to  prove  that  they 
are  endowed  with  this  power? 

Mrs.  B.  The  air  is  formed  of  particles  precisely 
of  the  same  nature  as  those  which  enter  into  the  com- 
position of  liquid  and  solid  bodies,  in  which  state  we 
have  a  proof  of  their  attraction. 

Emily.  It  is  then,  I  suppose,  owing  to  the  diff*er- 
ent  degrees  of  attraction  of  diff'erent  substances,  that 
they  are  hard  or  soft;  and  that  liquids  are  thick  or 
thin  ? 


22  GENERAL  PROPERTIES  OF  BODIES, 

Mrs.  B.  Yes ;  but  you  would  express  your  meati- 
ing  better  by  the  term  density,  which  denotes  the  de- 
gree of  closeness  and  compactness  of  the  particles  of 
a  body :  thus  you  may  say,  both  of  solids  and  of  li- 
quids, that  the  stronger  the  cohesive  attraction,  the 
greater  is  the  density  of  the  body.  In  philosophical 
language,  density  is  said  to  be  that  property  of  bodies 
by  which  they  contain  a  certain  quantity  of  matter, 
under  a  certain  bulk  or  magnitude.  Rarity  is  the 
cor»trary  of  density ;  it  denotes  the  thinness  and  sub- 
tlety of  bodies  :  thus  you  would  say  that  mercury  or 
quicksilver  was  a  very  dense  fluid  ;  ether,  a  very 
rare  one,  &c. 

Caroline.  But  how  are  we  to  judge  of  the  quantity 
of  matter  contained  in  a  certain  bulk? 

Mrs.  B.  By  the  weight:  under  the  same  bulk, 
bodies  are  said  to  be  dense  in  proportion  as  they  are 
heavy. 

Emily.  Then  we  may  say  that  metals  are  dense 
bodies,  wood  comparatively  a  rare  one,  &c.  But, 
Mrs.  B.,  when  the  particles  of  a  body  are  so  near  as 
to  attract  each  other,  the  effect  of  this  power  must 
increase  as  they  are  brought  by  it  closer  together ; 
so  that  one  would  suppose  that  the  body  would  gra- 
dually augment  in  density,  till  it  was  impossible  for 
its  particles  to  be  more  closely  united.  Now,  we 
know  that  this  is  not  the  case  ;  for  soft  bodies,  such 
as  cork,  sponge,  or  butter,  never  become,  in  conse- 
quence of  the  increasing  attraction  of  their  particles, 
as  hard  as  iron  ? 

Mrs.  B.  In  such  bodies  as  cork  and  sponge,  the 
particles  which  come  in  contact  are  so  few  as  to  pro- 
duce but  a  slight  degree  of  cohesion  :  they  are  po- 
rous bodies,  which,  owing  to  the  peculiar  arrange- 
ment of  their  particles,  abound  with  interstices  which 
separate  the  particles  ;  and  these  vacancies  are  filled 
with  air,  the  spring  or  elasticity  of  which  prevents 
the  closer  union  of  the  parts.  But  there  is  another 
fluid  much  more  subtle  than  air,  which  pervades  all 
bodies,  this  is  heat.     Heat  insinuates  itself  more  or 


GENERAL  PROPERTIES  OF  BODIES.  23 

less  between  the  particles  of  all  bodies,  and  forces 
them  asunder  ;  you  may  therefore  consider  heat,  and 
the  attraction  of  cohesion,  as  constantly  acting  in  op- 
position to  each  other. 

Emily.  The  one  endeavouring  to  rend  a  body  to 
pieces,  the  other  to  keep  its  parts  firmly  united. 

Mrs.  B.  And  it  is  this  struggle  between  the  con- 
tending forces  of  heat  and  attraction,  which  prevents 
the  extreme  degree  of  density  which  would  result 
from  the  sole  influence  of  the  attraction  of  cohesion. 

Emily.  The  more  a  body  is  heated  then,  the  more 
its  particles  will  be  separated. 

Mrs.  B,  Certainly  :  we  find  that  bodies  swell  or 
dilate  by  heat :  this  effect  is  very  sensible  in  butter, 
for  instance,  which  expands  by  the  application  of  heat, 
till  at  length  the  attraction  of  cohesion  is  so  far  dimi- 
nished that  the  particles  separate,  and  the  butter  be- 
comes liquid.  A  similar  effect  is  produced  by  heat 
on  metals,  and  all  bodies  susceptible  of  being  melted. 
Liquids,  you  know,  are  made  to  boil  by  the  appli- 
cation of  heat ;  the  attraction  of  cohesion  then  yields 
entirely  to  the  expansive  po>ver ;  the  particles  are 
totally  separated  and  converted  into  steam  or  va- 
pour. But  the  agency  of  heat  is  in  no  body  more 
sensible  than  in  air,  which  dilates  and  contracts  by 
its  increase  or  diminution  in  a  very  remarkable  de- 
gree. 

Emily.  The  effects  of  heat  appear  to  be  one  of 
the  most  interesting  parts  of  natural  philosophy. 

Mrs.  B.  That  is  true  ;  but  heat  is  so  intimately 
connected  with  chemistry,  that  you  must  allow  me  to 
defer  the  investigation  of  its  properties  till  you  be- 
come acquainted  with  that  science.  To  return  to  its 
antagonist,  the  attraction  of  cohesion  ;  it  is  this  pow- 
er which  restores  to  vapour  its  liquid  form,  which 
unites  it  into  drops  when  it  falls  to  the  earth  in  a  show- 
er of  rain,  which  gathers  the  dew  into  brilliant  gems 
on  the  blades  of  grass. 

Emily.  And  I  have  often  observed  that  after  a 
shower,  the  water  collects  into  large  drops  on  the 


'24  GENERAL  PROPERTIES  OF  BODIES. 

leaves  of  plants  ;  but  I  cannot  say  that  I  perfectly  unr 
derstand  how  the  attraction  of  cohesion  produces  this 
effect. 

Mrs.  B.  Rain  does  not  fall  from  the  clouds  in  the 
form  of  drops,  but  in  that  of  mist  or  vapour,  which  is 
composed  of  very  small  watery  particles  ;  these,  in 
their  descent,  mutually  attract  each  other,  and  those 
that  are  sufficiently  near  in  consequence  unite  and 
form  a  drop,  and  thus  the  mist  is  transformed  into  a 
shower.  The  dew  also  was  originally  in  a  state  of 
vapour,  but  is,  by  the  mutual  attraction  of  the  parti- 
cles, formed  into  small  globules  on  the  blades  of  grass  : 
in  a  similar  manner  the  rain  upon  the  leaf  collects  in- 
to large  drops,  which,  when  they  become  too  heavy 
for  the  leaf  to  support,  fall  to  the  ground. 

Emily.  All  this  is  wonderfully  curious !  I  am  al- 
most bewildered  with  surprise  and  admiration  at  the 
number  of  new  ideas  I  have  already  acquired. 

Mrs.  B.  Every  step  that  you  advance  in  the  pur- 
suit of  natural  science,  will  fill  your  mind  with  admi- 
ration and  gratitude  towards  its  Divine  Author.  In 
the  study  of  natural  philosophy,  we  must  consider 
ourselves  as  reading  the  book  of  nature,  in  which  the 
bountiful  goodness  and  wisdom  of  God  is  revealed  to 
all  mankind  ;  no  study  can  then  tend  more  to  purify 
the  heart,  and  raise  it  to  a  religious  contemplation  of 
the  Divine  perfections. 

There  is  another  curious  effect  of  the  attraction  of 
cohesion  which  I  must  point  out  to  you.  -  It  enables 
liquids  to  rise  above  their  level  in  capillary  tubes  : 
these  are  tubes  the  bores  of  which  are  so  extremely 
small  that  liquids  ascend  within  them,  from  the  cohe- 
sive attraction  between  the  particles  of  the  liquid  and 
the  interior  surface  of  the  tube.  Do  you  perceive 
the  water  rising  above  its  level  in  this  small  glass 
tube,  which  I  have  immersed  in  a  goblet  full  of  water  ? 

Emily.  Oh  yes  ;  I  see  it  slowly  creeping  up  the 
tube,  but  now  it  is  stationary  :  will  it  rise  no  higher  ? 

Mrs.  B.  No ;  because  the  cohesive  attraction  be- 
tween the  water  and  the  internal  surface  of  the  tube 


GENERAL  PROPERTIES  OF  BODIES.  26 

is  now  balanced  by  the  weight  of  the  water  within  it : 
if  the  bore  of  the  tube  were  narrower  the  water 
would  rise  higher;  and  if  you  immerse  several  tubes 
of  bores  of  different  sizes,  you  will  see  it  rise  to  differ- 
ent heights  in  each  of  them.  In  making  this  expe- 
riment you  should  colour  the  water  with  a  little  red 
wine,  in  order  to  render  the  effect  more  obvious. 

All  porous  substances,  such  as  sponge,  bread,  linen, 
&c.,  may  be  considered  as  collections  of  capillary 
tubes  :  if  you  dip  one  end  of  a  lump  of  sugar  into  wa- 
ter, the  water  will  rise  in  it,  and  wet  it  considerably 
above  the  surface  of  that  into  which  you  dip  it. 

Emily.  In  making  tea  I  have  often  observed  that 
effect,  without  being  able  to  account  for  it, 

Mrs.  B.  Now  that  you  are  acquaintted  with  the 
attraction  of  cohesion,  I  must  endeavour  to  explain  to 
you  that  oi  Gravitation,  which  is  a  modification  of  the 
same  power  ;  the  first  is  perceptible  only  in  very  mi- 
nute particles,  and  at  very  small  distances  ;  the  other 
acts  on  the  largest  bodies,  and  extends  to  immense 
distances. 

Emily.  You  astonish  me :  surely  you  do  not  mean 
to  say,  that  large  bodies  attract  each  other. 

Mrs.  B.  Indeed  I  do  :  let  us  take,  for  example, 
one  of  the  largest  bodies  in  nature,  and  observe  whe- 
ther it  does  not  attract  other  bodies.  What  is  it  that 
occasions  the  fall  of  this  book,  when  I  no  longer  sup- 
port it? 

Emily.  Can  it  be  the  attraction  of  the  earth  ?  I 
thought  that  all  bodies  had  a  natural  tendency  to  fall. 

Mrs.  B.  They  have  a  natural  tendency  to  fall,  it 
is  true  ;  but  that  tendency  is  produced  entirely  by 
the  attraction  of  the  earth  :  the  earth  being  so  much 
larger  than  any  body  on  its  surface,  forces  every  body, 
which  is  not  supported,  to  fall  upon  it 

Emily.  If  the  tendency  which  bodies  U,ave  to  fall 
results  from  the  earth's  attractive  power,  the  earth 
itself  can  have  no  such  tendency,  since  it  cannot  at- 
tract itself,  and  therefore  it  requires  no  support  to 
prevent  it  from  falling.  Yet  the  idea  that  bodies  do 
3 


Jb  GENERAL  PROPERTIES  OJP  BODIES. 

not  fall  of  their  own  accord,  but  that  they  are  drawn 
towards  the  earth  by  its  attraction,  is  so  new  and 
strange  to  me,  that  I  know  not  how  to  reconcile  my- 
self to  it. 

Mrs.  B.  When  you  are  accustomed  to  consider  the 
fall  of  bodies  as  depending  on  this  cause,  it  will  ap- 
pear to  you  as  natural,  and  surely  much  more  satisfac- 
tory, than  if  the  cause  of  their  tendency  to  fall  were 
totally  unknown.  Thus  you  understand,  that  all 
matter  is  attractive,  from  the  smallest  particle  to  the 
largest  mass  ;  and  that  bodies  attract  each  other  with 
a  force  proportional  to  the  quantity  of  matter  they 
contain. 

Emily.  I  do  not  perceive  any  difference  between 
the  attraction  of  cohesion  and  that  of  gravitation  ;  is 
it  not  because  every  particle  of  matter  is  endowed 
with  an  attractive  power,  that  large  bodies,  consist- 
ing of  a  great  number  of  particles,  are  so  strongly  at- 
tractive ? 

Mrs.  B.  True.  There  is,  however,  this  differ- 
ence between  the  attraction  of  particles  and  that  of 
masses,  that  the  former  is  stronger  than  the  latter,  in 
proportion  to  the  quantity  of  matter.  Of  this  you 
have  an  instance  in  the  attraction  of  capillary  tubes, 
in  which  liquids  ascend  by  the  attraction  of  cohesion, 
in  opposition  to  that  of  gravity.  It  is  on  this  account 
that  it  is  necessary  that  the  bore  of  the  tube  should  be 
extremely  small;  for  if  the  column  of  water  within 
the  tube  is  not  very  minute,  the  attraction  would  not 
be  able  either  to  raise  or  support  its  weight,  in  oppo- 
sition to  that  of  gravity. 

You  may  observe,  also,  that  all  solid  bodies  are 
enabled  by  the  force  of  the  cohesive  attraction  of 
their  particles  to  resist  that  of  gravity,  which  would 
otherwise  disunite  them,  and  bring  them  to  a  level 
with  the  ground,  as  it  does  in  the  case  of  liquids,  the 
cohesive  attraction  of  which  is  not  sufficient  to  enable 
it  to  resist  the  power  of  gravity. 

Emily.     And  some  solid  bodies  appear  to  be  of  this 


GENERAL  PROPERTIES  OF  BODIES.  27 

nature,  as  sand  and  powder  for  instance  ;  there  is  no 
attraction  ofcohesion  between  their  particles  ? 

Mrs.  B.  Every  grain  of  powder  or  sand  is  com- 
posed of  a  great  number  of  other  more  minute  parti- 
cles, tirmly  united  by  the  attraction  ofcohesion  ;  but 
amongst  the  separate  grains  there  is  no  sensible  at- 
traction, because  they  are  not  in  sufficiently  close 
contact. 

Emily.     Yet  they  actually  touch  each  other  ? 

Mrs.  B.  The  surf<ice  of  bodies  is  in  general  so 
rough  and  uneven,  that  when  in  actual  contact,  they 
touch  each  other  only  by  a  ^qw  points.  Thus,  if  I 
lay  upon  the  table  this  book,  the  binding  of  which  ap- 
pears perfectly  smooth,  yet  so  few  of  the  particles  of 
its  under  surface  come  in  contact  with  the  table,  that 
no  sensible  degree  of  cohesive  attraction  takes  place  ; 
for  you  see,  that  it  does  not  stick,  or  cohere  to  the 
table,  and  I  find  no  difficulty  in  lifting  it  off. 

It  is  only  when  surfaces  perfectly  flat  and  well  po- 
lished are  placed  in  contact,  that  the  particles  ap- 
proach in  sufficient  number,  and  closely  enough  to 
produce  a  sensible  degree  of  cohesive  attraction* 
Here  are  two  hemispheres  of  polished  metal,  I  press 
their  flat  surfaces  together,  having  previously  inter- 
posed a  {qw  drops  of  oil,  to  fill  up  every  little  porous 
vacancy.     Now  try  to  separate  them. 

Emily.  It  requires  an  eflbrt  beyond  my  strength, 
though  there  are  handles  for  the  purpose  of  pulling 
them  asunder.  Is  the  firm  adhesion  of  the  two 
hemispheres  merely  owing  to  the  attraction  of  cohe- 


sion 


Mrs.  B.  There  is  no  force  more  powerful,  since 
it  is  by  this  that  the  particles  of  the  hardest  bodies 
are  held  together.  It  would  require  a  weight  of  se- 
veral pounds  to  separate  these  hemispheres. 

Emily.  In  making  a  kaleidoscope,  I  recollect  that 
the  two  plates  of  glass,  which  were  to  serve  as  mir- 
rors, stuck  so  fast  together,  that  I  imagined  some  of 
the  gum  I  had  been  using  had  by  chance  been  inter- 
posed between  them ;  but  now  I  make  no  doubt  but 


28  GENERAL  PROPERTIES  OF  BODIES. 

that  it  was  their  own  natural  cohesive  attractioii 
which  produced  this  effect. 

Mrs.  B.  Very  probably  it  was  so  ;  for  plate-glass 
has  an  extremely  smooth  flat  surface,  admitting  of  the 
contact  of  a  great  number  of  particles,  between  two 
plates,  laid  one  over  the  other. 

Emily.  But,  Mrs.  B.,  the  cohesive  attraction  of 
some  bodies  is  much  greater  than  that  of  others  ; 
thus  glue,  gum,  and  paste,  cohere  with  singular  tena- 
city. 

Mrs.  B.  That  is  owing  to  the  peculiar  chemical 
properties  of  those  bodies,  independently  of  their  co- 
hesive attraction. 

There  are  some  other  kinds  or  modifications  of  at- 
traction peculiar  to  certain  bodies  ;  namely,  that  of 
magnetism,  and  of  electricity  ;  but  we  shall  confine 
our  attention  merely  to  the  attraction  of  cohesion  and 
of  gravity  ;  the  examination  of  the  latter  we  shall  re- 
sume at  our  next  meeting. 


CONVERSATION  11. 


ON  THE  ATTRACTION  OF  GRAVITY. 

Attraction  of  Gravitation,  continued. — Of  Weight. — 
Of  the  Fall  of  Bodies. — Of  the  Resistance  of  the  Air. 
— Of  the  Ascent  of  Light  Bodies. 

EjMILY.  I  have  related  to  my  sister  Caroline  all 
that  you  have  taught  me  of  natural  philosophy,  and 
she  has  been  so  much  delighted  by  it,  that  she  hopes 
you  will  have  the  goodness  to  admit  her  to  your  les- 
sons. 

Mrs.  B.  Very  willingly ;  but  I  did  not  think  you 
had  any  taste  for  studies  of  this  nature,  Caroline? 

Caroline.  I  confess,  Mrs.  B.,  that  hitherto  I  had 
formed  no  very  agreeable  idea,  either  of  philosophy, 
or  philosophers  ;  but  what  Emily  has  told  me,  has 
excited  my  curiosity  so  much,  that  I  shall  be  highly 
pleased  if  you  will  allow  me  to  become  one  of  your 
pupils. 

Mrs.  B.  I  fear  that  I  shall  not  find  you  so  tract- 
ablie  a  scholar  as  Emily  ;  I  know  that  you  are  much 
biassed  in  favour  of  your  own  opinions. 

Caroline.  Then  you  will  have  the  greater  meri{  in 
reforming  them,  Mrs.  B.  ;  and  after  all  the  wonders 
that  Emily  has  related  to  me,  I  think  I  stand  but  little 
chance  against  you  and  your  attractions. 

Mrs.  B.  You  will,  1  doubt  not,  advance  a  number 
of  objections ;  but  these  I  shall  willingly  admit,  as 
they  will  be  a  means  of  elucidating  the  subject. 
Emily,  do  you  recollect  the  names  of  the  general  pro- 
perties of  bodies? 

3* 


30  ON  THE  ATTRACTION  OF  GRAVITY. 

Emily.  Impenetrability,  extension,  figure,  divisi- 
bility, inertia,  and  attraction. 

Mrs,  B.  Very  well.  You  must  remember  that 
these  are  properties  common  to  all  bodies,  and  of 
which  they  cannot  be  deprived  ;  all  other  properties  of 
bodies  are  called  accidental,  because  they  depend  on 
the  relation  or  connexion  of  one  body  to  another. 

Caroline.  Yet  surely,  Mrs.  B.,  there  are  other 
properties  which  are  essential  to  bodies,  besides  those 
you  have  enumerated.  Colour  and  weight,  for  in- 
stance, are  common  to  all  bodies,  and  do  not  arise 
from  their  connexion  with  each  other,  but  exist  in 
the  bodies  themselves ;  these,  therefore,  cannot  be 
accidental  qualities  ? 

Mrs.  B.  I  beg  your  pardon  ;  these  properties  do 
not  exist  in  bodies  independently  of  their  connexion 
with  other  bodies. 

Caroline.  What  I  have  bodies  no  weight?  Does 
not  this  table  weigh  heavier  than  this  book;  and,  if 
one  thing  weighs  heavier  than  another,  must  there 
not  be  such  a  thing  as  weight? 

Mrs.  B.  No  doubt :  but  this  property  does  not  ap- 
pear to  be  essential  to  bodies  ;  it  depends  upon  their 
connexion  with  each  other.  Weight  is  an  effect  of 
the  power  of  attraction,  without  which  the  table  and 
the  book  would  have  no  weight  whatever. 

Emily.  I  think  1  understand  you  ;  is  it  not  the  at- 
traction of  gravity,  which  makes  bodies  heavy  ? 

Mrs.  B.  You  are  right.  I  told  you  that  the  at- 
traction of  gravity  was  proportioned  to  the  quantity  of 
matter  which  bodies  contained  ;  now  the  earth  con- 
sisting of  a  much  greater  quantity  of  matter  than  any 
body  upon  its  surface,  the  force  of  its  attraction  must 
necessarily  be  greatest,  and  must  draw  every  thing 
towards  it;  in  consequence  of  which,  bodies  that  are 
unsupported  fall  to  the  ground,  whilst  those  that  are 
supported  press  upon  the  object  which  prevents 
their  fall,  with  a  weight  equal  to  the  force  with 
which  they  gravitate  towards  the  earth. 

Caroline.     The  same  cause  then  which  occasion? 


ON  THE  ATTRACTION  OP  GRAVITr.      31 

the  fall  of  bodies,  produces  also  their  weight.  It  was 
very  dull  in  me  not  to  understand  this  before,  as  it  is 
the  natural  and  necessary  consequence  of  attraction  ; 
but  the  idea  that  bodies  were  not  really  heavy  of 
themselves,  appeared  to  me  quite  incomprehensible. 
But,  Mrs.  B.,  if  attraction  is  a  property  essential  to 
matter,  weight  must  be  so  likewise  ;  for  how  can  one 
exist  without  the  other  ? 

Mrs.  B.  Suppose  there  were  but  one  body  exist- 
ing in  universal  space,  what  would  its  weight  be  ? 

Caroline.  That  would  depend  upon  its  size  ;  or, 
more  accurately  speaking,  upon  the  quantity  of  mat- 
ter it  contained. 

Emily.  No,  no  ;  the  body  would  have  no  weight, 
whatever  were  its  size  ;  because  nothing  would  at- 
tract it.     Am  1  not  right,  Mrs.  B.  ? 

Mrs.  B.  You  are  ;  you  must  allow,  therefore, 
that  it  would  be  possible  for  attraction  to  exist  with- 
out weigi.t ;  for  each  of  the  particles  of  which  the 
body  was  composed,  would  possess  the  power  of  at- 
traction ;  but  they  could  exert  it  only  amongst  them- 
selves ;  the  whole  mass,  having  nothing  to  attract,  or 
to  be  attracted  by,  would  have  no  weight. 

Caroline.  1  am  now  well  satisfied  that  weight  is 
not  essential  to  the  existence  of  bodies  ;  but  what 
have  you  to  object  to  colours,  Mrs.  B.  ;  you  will  not, 
I  think,  deny  that  they  really  exist  in  the  bodies 
themselves. 

Mrs.  B.  When  we  come  to  treat  of  the  subject  of 
colours,  I  trust  that  I  shall  be  able  to  convince  you, 
that  colours  are  likewise  accidental  qualities,  quite 
distinct  from  the  bodies  to  which  they  appear  to  belong. 

Caroline.  Ob  do  pray  explain  it  to  us  now,  I  am 
so  very  curious  to  know  how  that  is  possible. 

Mrs.  B.  Unless  we  proceed  with  some  degree  of 
order  and  method,  you  will  in  the  end  find  yourself 
but  little  the  wiser  for  all  you  learn.  Let  us  there- 
fore go  on  regularly,  and  make  ourselves  well  ac- 
quainted with  the  general  properties  of  bodies,  before 
we  proceed  further. 


32  ON   THE    ATTRACTION  OF  GRAVITY. 

Emily.  To  return,  then,  to  attraction,  (which  ap- 
pears to  me  by  far  the  most  interesting  of  them,  since 
it  belongs  equally  to  all  kinds  of  matter,)  it  must  be 
mutual  between  two  bodies;  and  if  so,  when  a  stone 
falls  to  the  earth,  the  earth  should  rise  part  of  the  way 
to  meet  the  stone  ? 

Mrs.  B.  Certainly  ;  but  you  must  recollect  that 
the  force  of  attraction  is  proportioned  to  the  quantity 
of  matter  which  bodies  contain,  and  if  you  consider 
the  difference  there  is  in  that  respect,  between  a 
stone  and  the  earth,  you  will  not  be  surprised  that 
you  do  not  perceive  the  earth  rise  to  meet  the  stone  ; 
for  though  it  is  true  that  a  mutual  attraction  takes 
place  between  the  earth  and  the  stone,  that  of  the 
latter  is  so  very  small  in  comparison  to  that  of  the 
former,  as  to  render  its  effect  insensible. 

Emily.  But  since  attraction  is  proportioned  to 
the  quantity  of  matter  which  bodies  contain,  why  do 
not  the  hills  attract  the  houses  and  churches  towards 
them  ? 

Caroline.  Heavens,  Emily,  what  an  idea  1  How 
can  the  houses  and  churches  be  moved,  when  they 
are  so  firmly  fixed  in  the  ground  ? 

Mrs.  B.  Emily's  question  is  not  absurd,  and  your 
answer,  Caroline,  is  perfectly  just  ;  but  can  you  tell 
lis  why  the  houses  and  churhes  are  so  firmly  fixed  in 
the  ground  ? 

Caroline.  I  am  afraid  I  have  answered  right  by 
mere  chance ;  for  1  begin  to  suspect  that  bricklayers 
and  carpenters  could  give  but  little  stability  to  theit 
buildings,  without  the  aid  of  attraction. 

Mrs.  B.  It  is  certainly  the  cohesive  attraction 
between  the  bricks  and  the  mortar,  which  enables 
them  to  build  walls,  and  these  are  so  strongly  attract- 
ed by  the  earth,  as  to  resist  every  other  impulse  ; 
otherwise  they  would  necessarily  move  towards  the 
hills  and  the  mountains  ;  but  the  lesser  force  must 
yield  to  the  greater.  There  are,  however,  some 
circumstances  in  which  the  attraction  of  a  large  body 
has  sensibly  counteracted   that  of  the   earth.      If, 


ON  THE  ATTRACTION  OF  GRAVITY.  33 

whilst  standing  on  the  declivity  of  a  mountain,  you 
hold  a  plumb-line  in  your  hand,  the  weight  will  not 
fall  perpendicular  to  the  earth,  but  incline  a  little  to- 
wards the  mountain  ;  and  this^  owing  to  the  lateral, 
or  sideways  attraction  of  the  mountain,  interfering 
with  the  perpendicular  attraction  of  the  earth. 

Emily.  But  the  size  of  a  mountain  is  very  trifling, 
compared  to  the  whole  earth  ? 

Mrs.  B.  Attraction,  you  must  recollect,  diminishes 
with  distance  ;  and  in  the  example  of  the  plumb-line, 
the  weight  suspended  is  considerably  nearer  to  the 
mountain  than  to  the  centre  of  the  earth. 

Caroline.  Pray,  Mrs.  B.,  do  the  two  scales  of  a 
balance  hang  parallel  to  each  other  ? 

Mrs.  B.  You  mean,  I  suppose,  in  other  words,  to 
inquire  whether  two  lines  which  are  perpendicular  to 
the  earth,  are  parellel  to  each  other  ?  I  believe  I 
guess  the  reason  of  your  question?  but  I  wish  you 
would  endeavour  to  answer  it  without  my  assistance. 

Caroline.  I  was  thinking  that  such  lines  must  both 
tend  by  gravity  to  the  same  point,  the  centre  of  the 
earth  ;  now  lines  tending  to  the  same  point  cannot  be 
parallel,  as  parallel  lines  are  always  at  an  equal  dis- 
tance from  each  other,  and  would  never  meet. 

Mrs.  B.  Very  well  explained  :  you  see  now  the 
use  of  your  knowledge  of  parallel  lines ;  had  you 
been  ignorant  of  their  properties,  you  could  not  have 
drawn  such  a  conclusion.  This  may  enable  you  to 
form  an  idea  of  the  great  advantage  to  be  derived 
even  from  a  slight  knowledge  of  geometry,  in  the  stu- 
dy of  natural  philosophy  ;  and  if,  after  I  have  made 
you  acquainted  with  the  first  elements,  you  should  be 
tempted  to  pursue  the  study,  I  would  advise  you  to 
prepare  yourselves  by  acquiring  some  knowledge  of 
geometry.  This  science  would  teach  you  that  lines 
which  fall  perpendicular  to  the  surface  of  a  sphere 
cannot  be  parallel,  because  they  would  all  meet,  if 
prolonged  to  the  centre  of  the  sphere  ;  while  lines 
that  fall  perpendicular  to  a  plane  or  flat  surface,  are 


34  ON   THE  ATTRACTION  OF  GRAVITY. 

always  parallel,  because,  if  prolonged,  they  would 
never  meet. 

Emily.  And  yet  a  pair  of  scales,  hanging  perpen- 
dicular to  the  earth,  aopear  parallel? 

Mrs.  B.  Because  the  sphere  is  so  large,  and  the 
scales  consequently  converge  so  little,  that  their  in- 
clination is  not  perceptible  to  our  senses  ;  if  we 
could  construct  a  pair  of  scales  whose  beam  would 
extend  several  degrees,  their  convergence  would  be 
very  obvious  ;  but  as  this  cannot  be  accomplished, 
let  us  draw  a  small  tigure  of  the  earth,  and  then  we 
may  make  a  pair  of  scales  of  the  proportion  wc 
please,  (fig.   1.  Plate  I.) 

Caroline.  This  figure  renders  it  very  clear  :  then 
two  bodies  cannot  fall  to  the  earth  in  parallel  lines  ? 

Mrs.  B.     Never. 

Caroline.  The  reason  that  a  heavy  body  falls 
quicker  than  a  light  one,  is,  I  suppose,  because  the 
earth  attracts  it  more  strongly  ? 

Mrs.  B.  The  earth,  it  is  true,  attracts  a  heavy 
body  more  than  a  light  one  ;  but  that  would  not 
make  the  one  fall  quicker  than  the  other. 

Caroline.  Yet,  since  it  is  attraction  that  occasions 
the  fall  of  bodies,  surely  the  more  a  body  is  attracted, 
the  more  rapidly  it  will  fall.  Besides,  experience 
proves  it  to  be  so.  Do  we  not  every  day  see  heavy 
bodies  fall  quickly,  and  light  bodies  slowly. 

Emily.  It  strikes  me,  as  it  does  Caroline,  that  as 
attraction  is  proportioned  to  the  quantity  of  matter, 
the  earth  must  necessarily  attract  a  body  which  con- 
' tains  a  great  quantity  more  strongly,  and  therefore 
bring  it  to  the  ground  sooner  than  one  consisting  of 
a  smaller  quantity. 

Mrs.  B.  You  must  consider,  that  if  heavy  bodies 
are  attracted  more  strongly  than  light  ones,  they  re- 
quire more  attraction  to  make  them  fall.  Remem- 
ber that  bodies  have  no  natural  tendency  to  fall,  any 
more  than  to  rise,  or  to  move  laterally,  and  that  they 
will  not  fall  unless  impelled  by  some  force  ;  now 
this  force  must  be  proportioned  to  the  quantity  of 


TLATE  I. 


Jij.   2. 


%•    1- 


ON  THE  ATTRACTION  OF  GRAVITY.  35 

matter  it  has  to  move :  a  body  consisting  of  1000 
particles  of  matter,  for  instance,  requires  ten  times  as 
much  attraction  to  bring  it  to  the  ground  in  the 
same  space  of  time  as  a  body  consisting  of  only  100 
particles. 

Caroline.  I  do  not  understand  that  ;  for  it  seems 
to  me,  that  the  heavier  a  body  is,  the  more  easily  and 
readily  it  falls. 

Emily.  I  think  I  now  comprehend  it :  let  me  try 
if  I  can  explain  it  to  Caroline.  Suppose  that  1  draw 
towards  me  two  weighty  bodies,  the  one  of  lOOlbs. 
the  other  of  lOOOlbs.,  must  I  not  exert  ten  times  as 
much  strength  to  draw  the  larger  one  to  me,  in  the 
same  space  of  time  as  is  required  for  the  smaller  one  ? 
Aij  if  the  earth  draws  a  body  of  lOOOlbs.  weight  to  it 
in  the  same  space  of  time  that  it  draws  a  body  of 
lOOlbs.,  does  it  not  follow  that  it  attracts  the  body  of 
lOOOlbs.  weight  with  ten  times  the  force  that  it  does 
that  of  lOOlbs.? 

Caroline.  1  comprehend  your  reasoning  perfectly ; 
but  if  it  were  so,  the  body  of  lOOOlbs.  weight,  and 
that  of  lOOlbs.  would  fall  with  the  same  rapidity; 
and  the  consequence  would  be,  that  all  bodies,  whe- 
ther light  or  heavy,  being  at  an  equal  distance  from 
the  ground,  would  fall  to  it  in  the  same  space  of  time  : 
now  it  is  very  evident  that  this  conclusion  is  absurd ; 
experience  eve-  stant  contradicts  it:  observe  how 
much  sooner  this  book  reaches  the  floor  than  this 
sheet  of  paper,  when  1  let  them  drop  together. 

Emily.  That  is  an  objection  I  cannot  answer.  I 
must  refer  it  to  you,  Mrs.  B. 

Mrs.  B.  I  trust  that  we  shall  not  find  it  insurmount- 
able. It  is  true  that,  according  to  the  laws  of  attrac- 
tion, all  bodies  at  an  equal  distance  from  the  earth, 
should  fall  to  it  in  the  same  space  of  time ;  and  this 
would  actually  take  place  if  no  obstacle  intervened  to 
impede  their  fall.  But  bodies  fall  through  the  air, 
and  it  is  the  resistance  of  the  air  which  makes  bodies 
of  different  density  fall  with  different  degrees  of  ve- 
locity.    They  must  all  force  their  way  through  the 


36  ox  THE  ATTRACTION  OT  GRAVITY. 

air,  but  dense  heavy  bodies  overcome  this  obstacle 
more  easily  than  rarer  and  lighter  ones. 

The  resistance  which  the  air  opposes  to  the  fall  of 
bodies  is  proportioned  to  their  surface,  not  to  their 
weight ;  the  air  being  inert,  cannot  exert  a  greater 
force  to  support  the  weight  of  a  cannon  ball,  than  it 
does  to  support  the  weight  of  a  ball  (of  the  same  size) 
made  of  leather  ;  but  the  cannon  ball  will  overcome 
this  resistance  more  easily,  and  fall  to  the  ground, 
consequently,  quicker  than  the  leather  ball. 

Caroline.  This  is  very  clear,  and  solves  the  diffi- 
culty perfectly.  The  air  offers  the  same  resistance 
to  a  bit  of  lead  and  a  bit  of  feather  of  the  same  size  ; 
yet  the  one  seems  to  meet  with  no  obstruction  in  its 
fall,  whilst  the  other  is  evidently  resisted  and  sup- 
ported for  some  time  by  the  air. 

Emily.  The  larger  the  surface  of  a  body,  then, 
the  more  air  it  covers,  and  the  greater  is  the  resist- 
ance it  meets  with  from  it. 

Mrs.  B.  Certainly  ;  observe  the  manner  in 
which  this  sheet  of  paper  falls  ;  it  floats  a  while  in  the 
air,  and  then  gently  descends  to  the  ground.  I  will 
roll  the  same  piece  of  paper  up  into  a  ball :  it  offers 
now  but  a  small  surface  to  the  air,  and  encounters 
therefore  but  little  resistance  :  see  how  much  more 
rapidly  it  falls. 

The  heaviest  bodies  may  be  made  to  float  a  while 
in  the  air,  by  making  the  extent  of  their  surface 
counterbalance  their  weight.  Here  is  some  gold, 
which  is  the  most  dense  body  we  are  acquainted 
^vith,  but  it  has  been  beaten  into  a  very  thin  leaf,  and 
offers  so  great  an  extent  of  surface  in  proportion  to  its 
weight,  that  its  fall,  you  see,  is  still  more  retarded  by 
the  resistance  of  the  air  than  that  of  the  sheet  of  paper. 

Caroline.  That  is  very  curious  ;  and  it  is,  I  sup- 
pose, upon  the  same  principle  that  iron  boats  may  be 
made  to  float  on  water  ? 

But,  Mrs.  B.,  if  the  air  is  a  real  body,  is  it  not  al- 
so subjected  to  the  laws  of  gravity  ? 

Mrs.  B,     Undoubtedly. 


OxV  THE  ATTRACTIOX  OF  GRAVITY.  3V 

Caroline.  Then  why  does  it  not,  like  all  other  bo- 
dies, fall  to  the  ground  ? 

Mrs.  B.  On  account  of  its  spring  or  elasticity. 
The  air  is  an  elastic  Jluid ;  a  species  of  bodies,  the 
peculiar  property  of  which  is  to  resume,  after  com- 
pression, their  original  dimensions  ;  and  you  must 
consider  the  air  of  which  the  atmosphere  is  compo- 
sed as  existing  in  a  state  of  compression,  for  its  parti- 
cles being  drawn  towards  the  earth  by  gravity,  are 
brought  closer  together  than  they  would  otherwise 
be,  but  the  spring  or  elasticity  of  the  air  by  which  it 
endeavours  to  resist  compression,  gives  it  a  constant 
tendency  to  expand  itself,  so  as  to  resume  the  dimen- 
sions it  would  naturally  have,  if  not  under  the  influ- 
ence of  gravit3^  The  air  may  therefore  be  said  con- 
stantly to  struggle  with  the  power  of  gravity  without 
being  able  to  overcome  it.  Gravity  thus  confines  the 
air  to  the  regions  of  our  globe,  whilst  its  elasticity 
prevents  it  from  falling  like  other  bodies  to  the 
ground. 

Emily.  The  air  then  is,  I  suppose,  thicker,  or  1 
should  rather  say  more  dense,  near  the  surface  of  the 
earth  than  in  the  higher  regions  of  the  atmosphere  ; 
for  that  part  of  the  air  which  is  nearer  the  surface  of 
the  earth,  must  be  most  strongly  attracted. 

Mrs.  B.  The  diminution  of  the  force  of  gravity, 
at  so  small  a  distance  as  that  to  which  the  atmosphere 
extends  (compared  with  the  size  of  the  earth)  is  so 
inconsiderable  as  to  be  scarcely  sensible  ;  but  the 
pressure  of  the  upper  parts  of  the  atmosphere  on 
those  beneath,  renders  the  air  near  the  surface  of  the 
earth  much  more  dense  than  the  upper  regions. 
The  pressure  of  the  atmosphere  has  been  compared 
to  that  of  a  pile  of  fleeces  of  wool,  in  which  the  low- 
er fleeces  are  pressed  together  by  the  weight  of 
those  above  ;  these  lie  light  and  loose,  in  proportion 
as  they  approach  the  uppermost  fleece,  which  re- 
ceives no  external  pressure,  and  is  confined  merely 
by  the  force  of  its  own  gravity. 

Caroline.    It  has  just  occurred  to  me  that  there  are 
4 


38  ON  THE  ATTRACTION  OF  GRAVITY. 

some  bodies  which  do  not  gravitate  towards  the  earth. 
Smoke  and  steam,  for  instance,  rise  instead  of  falling. 

Mrs.  B.  It  is  still  gravity  which  produces  their 
ascent ;  at  least,  were  that  power  destroyed,  these 
bodies  would  not  rise. 

Caroline.  I  shall  be  out  of  conceit  with  gravity,  if 
it  is  so  inconsistent  in  its  operations. 

Mrs.  B.  There  is  no  difficulty  in  reconciling  this 
apparent  inconsistency  of  effect.  The  air  near  the 
earth  is  heavier  than  smoke,  steam,  or  other  vapours  ; 
it  consequently  not  only  supports 'these  light  bodies, 
but  forces  them  to  rise,  till  they  reach  a  part  of  the 
atmosphere,  the  weight  of  which  is  not  greater  than 
their  own,  and  then  they  remain  stationary.  Look 
at  this  basin  of  water  ;  why  does  the  piece  of  paper 
which  I  throw  into  it  float  on  the  surface  ? 

Emily.  Because,  being  lighter  than  the  water,  it 
is  supported  by  it. 

Mrs.  B.  And  now  that  I  pour  more  water  into 
the  basin,  why  does  the  paper  rise  ? 

Emily.  The  water  being  heavier  than  the  paper, 
gets  beneath  it,  and  obliges  it  to  rise. 

Mrs.  B.  In  a  similar  manner  are  smoke  and  va- 
pour forced  upwards  by  the  air  ;  but  these  bodies  do 
not,  like  the  paper,  ascend  to  the  surface  oi  the  fluid, 
because,  as  we  observed  before,  the  air  being  thinner 
and  lighter  as  it  is  more  distant  from  the  earth,  vapours 
rise  only  till  they  attain  a  region  of  air  of  their  own 
density.  Smoke,  indeed,  ascends  but  a  very  little  way; 
it  consists  of  minute  particles  of  fuel  carried  up  by  a 
current  of  heated  air  from  the  fire  below :  heat,  you 
recollect,  expands  all  bodies ;  it  consequently  rarefies 
air,  and  renders  it  lighter  than  the  colder  air  of  the 
atmosphere ;  the  heated  air  from  the  fire  carries  up 
with  it  vapour  and  small  particles  of  the  combustible 
materials  which  are  burning  in  the  fire.  When  this 
current  of  hot  air  is  cooled  by  mixing  with  that  of  the 
atmosphere,  the  minute  particles  of  coal  or  other  com- 
bustible fall,  and  it  is  this  which  produces  the  small 


ON  THE  ATTRACTION  OF  GRAVITY.      3d 

black  flakes  which  render  the  air  and  every  thing  in 
contact  with  it,  in  London,  so  dirty. 

Caroline.  You  must,  however,  allow  me  to  make 
one  more  objection  to  the  universal  gravity  of  bodies  ; 
which  is  the  ascent  of  air  balloons,  the  materials  of 
which  are  undoubtedly  heavier  than  air  ;  how,  there- 
tbre,  can  they  be  supported  by  it  ? 

Mrs.  B.  1  admit  that  the  materials  of  which  bal- 
loons are  made  are  heavier  than  the  air;  but  the  air 
with  which  they  are  tilled  is  an  elastic  fluid,  of  a  dif- 
ferent nature  from  the  atmospheric  air,  and  consider- 
ably lighter  :  so  that,  on  the  whole,  the  balloon  is 
lighter  than  the  air  which  it  displaces,  and  conse- 
quently will  rise,  on  the  same  principle  as  smoke 
and  vapour.  Now,  Emily,  let  me  hear  if  you  can  ex- 
plain how  the  gravity  of  bodies  is  modified  by  the  ef- 
fect of  the  air  ? 

Emily.  The  air  forces  bodies  which  are  lighter 
than  itself  to  ascend  ;  those  that  are  of  an  equal 
weight  will  remain  stationary  in  it ;  and  those  that 
are  heavier  will  descend  through  it :  but  the  air  will 
have  some  eifect  on  these  last ;  for  if  they  are  not 
much  heavier,  they  will  with  difficulty  overcome 
the  resistance  they  meet  with  in  passing  through  it, 
they  will  be  borne  up  by  it,  and  their  fall  will  be 
more  or  less  retarded. 

Mrs.  B.  Very  well.  Observe  how  slowly  this 
light  feather  falls  to  the  ground,  while  a  heavier  bo- 
dy, like  this  marble,  overcomes  the  resistance  which 
the  air  makes  to  its  descent  much  more  easily,  and  its 
fall  is  proportionally  more  rapid.  1  now  throw  a 
pebble  into  this  tub  of  water  ;  it  does  not  reach  the 
bottom  near  so  soon  as  if  there  were  no  water  in  the 
tub,  because  it  meets  with  resistance  from  the  water. 
Suppose  that  we  could  empty  the  tub,  not  only  of 
water,  but  of  air  also,  the  pebble  would  then  fall 
quicker  still,  as  it  would  in  that  case  meet  with  no 
resistance  at  all  to  counteract  its  gravity. 

Thus  you  see  that  it  is  not  the  differe^it  degrees  of 
gravity,  but  the  resistance  of  the  air,  wnich  prevents 


40  ON  THE  ATTRACTION  OF  GRAVITY. 

bodies  of  different  weight  from  falling  with  equal  ve- 
locities ;  if  the  air  did  not  bear  up  the  feather,  it 
would  reach  the  ground  as  soon  as  the  marble. 

Caroline.  I  make  no  doubt  that  it  is  so  ;  and  yet 
I  do  not  feel  quite  satisfied.  I  wish  there  was  any 
place  void  of  air,  in  which  the  experiment  could  be 
made. 

Mrs.  B.  If  that  proof  will  satisfy  your  doubts,  I 
can  give  it  you.  Here  is  a  machine  called  an  air 
punip^  (fig.  2.  pi.  1.)  by  means  of  which  the  air  may 
be  expelled  from  any  close  vessel  which  is  placed 
over  this  opening,  through  which  the  air  is  pumped 
out.  Glasses  of  various  shapes,  usually  called  receiv- 
ers, are  employed  for  this  purpose.  We  shall  now 
exhaust  the  air  from  this  tall  receiver  which  is  placed 
over  the  opening,  and  we  shall  find  that  bodies  of 
whatever  weight  or  size  within  it,  will  fall  from  the 
top  to  the  bottom  in  the  same  space  of  time. 

Caroline.  Oh,  I  shall  be  delighted  with  this  expe- 
riment! what  a  curious  machine!  how  can  you  put 
the  two  bodies  of  different  weight  within  the  glass, 
without  admitting  the  air. 

Mrs.  B.  A  guinea  and  a  feather  are  already  pla- 
ceji  there  for  the  purpose  of  the  experiment:  here  is, 
you  see,  a  contrivance  to  fasten  them  in  the  upper 
part  of  the  glass  ;  as  soon  as  the  air  is  pumped  out,  I 
shall  turn  this  little  screw,  by  which  means  the  brass 
plates  which  support  them  will  be  inclined,  and  the 
two  bodies  will  fall. — Now  1  believe  I  have  pretty 
well  exhausted  the  air. 

Caroline.  Fray  let  me  turn  the  screw. — I  declare, 
they  both  reached  the  bottom  at  the  same  instant  ? 
Did  you  see,  Emily,  the  feather  appeared  as  heavy 
as  the  guinea  ? 

Emily.  Exactly  ;  and  fell  just  as  quickly.  How 
wonderful  this  is  !  what  a  number  of  entertaining  ex- 
periments might  be  made  with  this  machine  I 

Mrs.  B.  No  doubt  there  are  a  great  variety  ;  but 
we  shall  reserve  them  to  elucidate  the  subjects  to 
which  they  relate  :  if  I  had  not  explained  to  you  why 


ON  THE  ATTRACTION  OP  GRAVITY.  4t 

the  guinea  and  the  feather  fell  with  equal  velocity, 
you  would  not  have  been  so  well  pleased  with  the 
experiment. 

Emihj.  I  should  have  been  as  much  surprised, 
but  not  so  much  interested  ;  besides,  experiments 
help  to  imprint  on  the  memory  the  facts  they  are  in- 
tended to  illustrate  ;  it  will  be  better  therefore  for  us 
to  restrain  our  curiosity,  and  wait  for  other  experi- 
ments in  their  proper  places. 

Caroline.  Pray  by  what  meansis  the  air  exhaust- 
ed in  this  receiver  ? 

Mrs.  B.  You  must  learn  something  of  mechanics 
in  order  to  understand  tlte  construction  of  a  pump. 
At  our  next  meeting,  therefore,  I  shall  endeavour  to 
make  you  acquainted  with  the  law^  of  motion,  as  an 
introduction  to  that  subject. 


4* 


CONVERSATION  III. 


ON   THE  LAWS   OF   MOTION. 

Of  Motion. —  Of  the  Inertia  of  Bodies.— Of  Force  to 
Produce  Motion. — Direction  of  Motion. — Velocity, 
Absolute  and  Relative. — Uniform  Motion. — Retard- 
ed Motion. — Accelerated  Motion. — Velocity  of  Fall- 
ing  Bodies. — .Momentum. — Action  and  Re-action 
Equal.— Elasticity  of  Bodies. — Porosity  of  Bodies. 
— Reflected  Motion. — Angles  of  Incidence  and  Re- 
flection.  "**- 

MRS.  B.  The  science  of  mechanics  is  founded  on 
the  laws  of  motion ;  it  will  therefore  be  necessary  to 
make  you  acquainted  with  these  laws  before  we  exa- 
mine the  mechanical  powers.  Tell  me,  Caroline, 
what  do  you  understand  by  the  word  motion  ? 

Caroline.  I  think  I  understand  it  perfectly,  though 
I  am  at  a  loss  to  describe  it.  Motion  is  the  act  of  mo- 
ving about,  going  from  one  place  to  another,  it  is  the 
contrary  of  remaining  at  rest. 

Mrs.  B.  Very  well.  Motion  then  consists  in  a 
change  of  place;  a  body  is  in  motion  whenever  it  is 
changing  its  situation  with  regard  to  a  fixed  point. 

Now,  since  we  have  observed  that  one  of  the  general 
properties  of  bodies  is  Inertia,  that  is,  an  entire  pas- 
siveness  either  with  r^ard  to  motion  or  rest,  it  fol- 
lows that  a  body  cannot  move  without  being  put  into 
motion  :  the  power  which  puts  a  body  into  motion  is 
called  force ;  thus  the  stroke  of  the  hammer  is  the 


ON  THE  LAWS  OF  MOTION.  43 

force  which  drives  the  nail  ;  the  pulling  of  the  horse 
that  which  draws  the  carriage,  &c.  Force  then  is 
the  cause  which  produces  niotion. 

Emily.  And  may  we  not  sa\  that  gravity  is  the 
force  which  occasions  the  fall  of  bodies  ? 

Mrs.  B.  Undoubtedly.  I  had  given  you  the  most 
familiar  illustrations  in  order  to  render  the  explana- 
tion clear  ;  but  since  you  seek  for  more  scientific 
examples,  you  may  say  that  cohesion  is  the  force 
which  binds  the  particles  of  bodies  together,  and  heat 
that  which  drives  them  asunder. 

The  motion  of  a  body  acted  upon  by  a  single  force 
is  always  in  a  straight  line,  in  the  direction  in  which 
it  received  the  impulse. 

Caroline.  That  is  ver}'  natural  ;  for  as  the  body  is 
inert,  and  can  move  only  because  it  is  impelled,  it 
will  move  only  in  the  direction  in  which  it  is  impel- 
led. The  degree  of  quickness  with  which  it  moves 
must,  I  suppose,  also  depend  upon  the  degree  of  force 
with  which  it  is  impelled. 

Mrs.  B.  Yes  ;  the  rate  at  which  a  body  moves,  or 
the  shortness  of  the  time  which  it  takes  to  move  from 
one  place  to  another,  is  called  its  velocity  ;  and  it  is 
one  of  the  laws  of  motion  that  the  velocity  of  the  mo- 
ving body  is  proportional  to  the  force  by  which  it  is 
put  in  motion.  We  must  distinguish  between  abso- 
lute and  relative  velocity. 

The  velocity  of  a  body  is  called  absolute,  if  we  con- 
sider the  motion  of  the  body  in  space,  without  any 
reference  to  that  of  other  bodies.  When  for  in- 
stance a  horse  goes  fifty  miles  in  ten  hours,  his  velo- 
city is  five  miles  an  hour. 

The  velocity  of  a  body  is  termed  relative,  when 
compared  with  that  of  another  body  which  is  itself  in 
motion.  For  instance,  if  one  man  walks  at  the  rate 
of  a  mile  an  hour,  and  another  at  the  rate  of  two 
miles  an  hour,  the  relative  velocity  of  the  latter  is 
double  that  of  the  former  ;  but  the  absolute  velocity 
of  the  one  is  one  mile,  and  that  of  the  other  two 
miles  aa  hour. 


44  ON  THE  LAWS  OF  MOTION. 

Emily.  Let  me  see  if  1  understand  it — The  rela- 
tive velocity  of  a  body  is  the  degree  of  rapidity  of  its 
motion  compared  with  that  of  another  body  ;  thus,  if 
one  ship  sail  three  times  as  far  as  another  ship  in  the 
same  space  of  time,  the  velocity  of  the  former  is 
equal  to  three  times  that  of  the  latter. 

Mrs.  B.  The  general  rule  may  be  expressed  thus  : 
the  velocity  of  a  body  is  measured  by  the  space  over 
which  it  moves,  divided  by  the  time  which  it  employs 
in  that  motion  :  thus,  if  you  travel  one  hundred  miles 
in  twenty  hours,  what  is  your  velocity  in  each  hour  ? 

Emily.  I  must  divide  the  space,  which  is  one 
hundred  miles,  by  the  time,  which  is  twenty  hours, 
and  the  answer  will  be  five  miles  an  hour.  Then, 
Mrs.  B.,  may  we  not  reverse  this  rule  and  say,  that 
the  time  is  equal  to  the  space  divided  by  the  veloci- 
ty ;  since  the  space  one  hundred  miles,  divided  by 
the  velocity  five  miles,  gives  twenty  hours  for  the 
time? 

Mrs.  B.  Certainly;  and  we  may  say  also  that 
space  is  equal  to  the  velocity  multiplied  by  the  time. 
Can  you  tell  me,  Caroline,  how  many  miles  you  will 
have  travelled,  if  your  velocity  is  three  miles  an 
hour  and  you  travel  six  hours  ? 

Caroline.  Eighteen  miles  ;  for  the  product  of  3 
multiplied  by  6,  is  18. 

Mrs.  B.  I  suppose  that  you  understand  what  is 
meant  by  the  terms  uniform^  accelerated  and  retarded 
motion. 

Emily.  I  conceive  uniform  motion  to  be  that  of  a 
body  whose  motion  is  regular,  and  at  an  equal  rate 
throughout ;  for  instance,  a  horse  that  goes  an  equal 
number  of  miles  every  hour.  But  the  hand  of  a 
watch  is  a  much  better  example,  as  its  motion  is  so 
regular  as  to  indicate  the  time. 

Mrs.  B.  You  have  a  right  idea  of  uniform  motion  ; 
but  it  would  be  more  correctly  expressed  by  saying, 
that  the  motion  of  a  body  is  uniform  w  hen  it  passes 
over  equal  spaces  in  equal  times.  Uniform  motion  is 
produced  by  a  force  having  acted  on  a  body  once, 


ON  THE  LAWS  OF  MOTION.  46 

and  having  ceased  to  act ;  as  ibr  instance,  the  stroke 
of  a  bat  on  a  cricket  ball. 

Caroline.  But  the  motion  of  a  cricket  ball  is  not 
uniform ;  its  velocity  gradaally  diminishes  till  it  falls 
to  the  ground. 

Mrs.  B.  Recollect  that  the  cricket  ball  is  inert, 
and  has  no  more  power  to  stop  than  to  put  itself  in 
motion;  if  it  falls,  therefore,  it  must  be  stopped  by 
some  force  superior  to  that  by  which  it  was  project- 
ed, and  which  destroys  its  motion. 

Caroline.  And  it  is  no  doubt  the  force  of  gravity 
which  counteracts  and  destroys  that  of  projection; 
but  if  there  were  no  such  power  as  gravity,  would 
the  cricket  ball  never  stop? 

Mrs.  B.  If  neither  gravity  nor  any  other  force, 
such  as  the  resistance  of  the  air,  opposed  its  motion, 
the  cricket  ball,  or  even  a  stone  thrown  by  the  hand, 
would  proceed  onwards  in  a  right  line,  and  with  a 
uniform  velocity,  for  ever. 

Caroline.  You  astonish  me  !  I  thought  that  it  was 
impossible  to  produce  perpetual  motion  ? 

Mrs.  B.  Perpetual  motion  cannot  be  produced  by 
art,  because  gravity  ultimately  destroys  all  motion  that 
human  powers  can  produce. 

Emily.  But  independently  of  the  force  of  gra- 
vity, I  cannot  conceive  that  the  little  motion  I  am 
capable  of  giving  to  a  stone  would  put  it  in  motion  for 
ever. 

Mrs.  B.  The  quantity  of  motion  you  communica- 
ted to  the  stone  would  not  influence  its  duration ;  if 
you  threw  it  with  little  force  it  would  move  slowly, 
for  its  velocity,  you  must  remember,  will  be  propor- 
tional to  the  force  with  which  it  is  projected  ;  but  if 
there  is  nothing  to  obstruct  its  passage,  it  will  conti- 
nue to  move  with  the  same  velocity,  and  in  the  same 
direction  as  when  you  first  projected  if. 

Caroline.  This  appears  to  me  quite  incomprehen- 
sible ;  we  do  not  meet  with  a  single  instance  of  it  in  na- 
ture. 

Mrs.  B.     I  beg  your  pardon.     When  you  come  to 


46  ON  THE  LAWS  OF  MOTION. 

study  the  motion  of  the  celestial  bodies,  you  will  llnd 
that  nature  abounds  with  examples  of  perpetual  mo- 
tion ;  and  that  it  conduces  as  much  to  the  harmony  of 
the  system  of  the  universe,  as  the  prevalence  of  it 
would  to  the  destruction  of  all  comfort  on  our  globe. 
The  wisdom  of  Providence  has  therefore  ordained 
insurmountable  obstacles  to  perpetual  motion  here 
below,  and  though  these  obstacles  often  compel  us  to 
contend  with  great  difficulties,  yet  there  results  from 
it  that  order,  regularity  and  repose,  so  essential  to  the 
preservation  of  all  the  various  beings  of  which  this 
world  is  composed. 

Now  can  you  tell  me  what  is  retarded  motion  ? 

Carolme.  Retarded  motion  is  that  of  a  body  which 
moves  every  moment  slower  and  slower  ;  thus  when 
I  am  tired  with  walking  fast,  I  slacken  my  pace  ;  or 
when  a  stone  is  thrown  upweirds,  its  velocity  is  gra- 
dually diminished  by  the  power  of  gravity. 

Mrs.  B.  Retarded  motion  is  produced  by  some 
force  acting  upon  the  body  in  a  direction  opposite  to 
that  which  lirst  put  it  in  motion  :  you  who  are  an  ani- 
mated being,  endowed  with  power  and  will,  may 
slacken  your  pace,  or  stop  to  rest  when  you  are 
tired  ;  but  inert  matter  is  mcapable  of  any  feeling  of 
fatigue,  can  never  slacken  its  pace,  and  never  stop, 
unless  retarded  or  arrested  in  its  course  by  some  op- 
posing force ;  and  as  it  is  the  laws  of  inert  bodies 
which  mechanics  treats  of,  I  prefer  your  illustration 
of  the  stone  retarded  in  its  ascent.  Now,  Emily,  it  is 
your  turn  ;  what  is  accelerated  motion? 

Emily.  Accelerated  motion,  I  suppose,  takes 
place  when  the  velocity  of  a  body  is  increased  ;  if 
you  had  not  objected  to  our  giving  such  active  bodies 
as  ourselves  as  examples,  I  should  say  that  my  mo- 
tion is  accelerated  if  I  change  my  pace  from  walking 
to  running.  1  cannot  think  of  any  instance  of  accele- 
rated motion  in  inanimate  bodies  ;  all  motion  of  inert 
matter  seems  to  be  retarded  by  gravity. 

Mrs.  B.  Not  in  all  cases  ;  for  the  power  of  gravi- 
tation sometimes  produces  accelerated  motion  ;   for 


ON  THE  LAWS  OF  MOTION.  47 

instance,  a  stone  falling  from  a  height  moves  with  a 
regularly  accelerated  motion. 

Emily.  True  ;  because  the  nearer  it  approaches 
the  earth,  the  more  it  is  attracted  by  it. 

Airs.  B.  You  have  mistaken  the  cause  of  its  acce- 
leration of  motion  ;  for  though  it  is  true  that  the  force 
of  gravity  increases  as  a  body  approaches  the  earth, 
the  difference  is  so  trifling  at  any  small  distance  from 
its  surface  as  not  to  be  perceptible. 

Accelerated  motion  is  produced  when  the  force 
which  put  a  body  in  motion  continues  to  act  upon  it 
during  its  motion,  so  that  its  motion  is  continually  in- 
creased. When  a  stone  falls  from  a  height,  the  im- 
pulse which  it  receives  from  gravity  during  the  first 
instant  of  its  fall,  would  be  sufficient  to  bring  it  to  the 
ground  with  a  uniform  velocity  :  for,  as  we  have  ob- 
served, a  body  having  been  once  acted  upon  by  a 
force,  will  continue  to  move  with  a  uniform  velocity; 
but  the  stone  is  not  acted  upon  by  gravity  merely  at 
the  first  instant  of  its  fall,  this  power  continues  to  im- 
pel it  during  the  whole  of  its  descent,  and  it  is  this 
continued  impulse  which  accelerates  its  motion. 

Emily.     1  do  not  quite  understand  that. 

Mrs.  B.  Let  us  suppose  that  the  instant  after  you 
have  let  fall  a  stone  from  a  high  tower,  the  force  of 
gravity  were  annihilated,  the  body  would  nevertheless 
continue  to  move  downwards,  for  it  would  have  re- 
ceived a  first  impulse  from  gravity,  and  a  body  once 
put  in  motion  will  not  stop  unless  it  meets  with  some 
obstacle  to  impede  its  course  ;  in  this  case  its  veloci- 
ty would  be  uniform,  for  though  there  would  be  no 
obstacle  to  obstruct  its  descent,  there  would  be  no 
force  to  accelerate  it. 

Emily.     That  is  very  clear. 

Mrs.  B.  Then  you  have  only  to  add  the  power  of 
gravity  constantly  acting  on  the  stone  during  its  de- 
scent, and  it  will  not  be  difficult  to  understand  that  its 
motion  will  become  accelerated,  since  the  gravity 
which  acts  on  the  stone  durins  the  first  instant  of  its 


48  ON  THE  LAWS  OF  MOTIOX. 

descent,  will  continue  in  force  every  instant  till  it 
reaches  the  ground.  Let  us  suppose  that  the  impulse 
given  by  gravity  to  the  stone  during  the  first  instant 
of  its  descent  be  equal  to  one,  the  next  instant  we 
shall  find  that  an  additional  impulse  gives  the  stone  an 
additional  velocity  equal  to  one,  so  that  the  accumu- 
lated velocity  is  now  equal  to  two ;  the  following  in- 
stant another  impulse  increases  the  velocity  to  three, 
and  so  on  till  the  stone  reaches  the  ground. 

Caroline.  Now  I  understand  it ;  the  effects  of  pre- 
ceding impulses  must  be  added  to  the  subsequent  ve- 
locities. 

Mrs.  B.  Yes  ;  it  has  been  ascertained,  both  by 
experiment  and  calculations,  which  it  would  be  too 
difficult  for  us  to  enter  into,  that  heavy  bodies  de- 
scending from  a  height,  by  the  force  of  gravity,  fall 
sixteen  feet  the  first  second  of  time,  three  times  that 
distance  in  the  next,  five  times  in  the  third  second, 
seven  times  in  the  fourth,  and  so  on,  regularly 
increasing  their  velocities  according  to  the  number  of 
seconds  during  which  the  body  has  been  falling. 

Einilij.  If  you  throw  a  stone  perpendicularly  up- 
wards, is  it  not  the  same  length  of  time  ascending  that 
it  is  descending  ? 

Mrs.  B.  Exactly ;  in  ascending,  the  velocity  is  di- 
minished by  the  force  of  gravity  ;  in  descending,  it  is 
accelerated  by  it. 

Caroline.  I  should  then  have  imagined  that  it 
would  have  f\dlen  quicker  than  it  rose  ? 

Mrs.  B.  You  must  recollect  that  the  force  with 
which  it  is  projected  must  be  taken  into  the  account ; 
and  that  this  force  is  overcome  and  destroyed  by  gra- 
vity before  the  body  falls. 

Caroline.  But  the  force  of  projection  given  to  a 
stone  in  throwing  it  upwards,  cannot  always  be  equal 
to  the  force  of  gravity  in  bringing  it  down  again,  for 
the  force  of  gravity  is  always  the  same,  whilst  the  de- 
gree of  impulse  given  to  the  stone  is  optional ;  I 
may  throw  it  up  gently,  or  with  violence. 


QN  THE  LAWS  OF  MOTION.  49 

Mrs,  B.  If  you  throw  it  gently,  it  will  not  rise 
high  ;  perhaps  only  sixteen  feet,  in  which  case  it  will 
fall  in  one  second  of  time.  Now  it  is  proved  by  ex- 
periment, that  an  impulse  requisite  to  project  a  body 
sixteen  ^QGi  upwards,  will  make  it  ascend  that  height 
in  one  second  ;  here  then  the  times  of  the  ascent  and 
descent  are  equal.  But  supposing  it  be  required  to 
throw  a  stone  twice  that  height,  the  force  must  be 
proportionally  greater. 

You  see  then,  that  the  impulse  of  projection  in 
throwing  a  body  upwards,  is  always  equal  to  the  ac- 
tion of  the  force  of  gravity  during  its  descent ;  and 
that  it  is  the  greater  or  less  distance  to  which  the 
body  rises,  that  makes  these  two  forces  balance  each 
other. 

I  must  now  explain  to  you  what  is  meant  by  the 
momentum  of  bodies.  It  is  the  force,  or  power,  with 
which  a  body  in  motion  strikes  against  another  body. 
The  momentum  of  a  body  is  composed  of  its  quantity 
of  matter,  multiplied  by  its  quantity  of  motion;  in 
other  words,  its  weight  and  its  velocity. 

Caroline.  The  quicker  a  body  moves,  the  greater, 
no  doubt,  must  be  the  force  with  which  it  would  strike 
against  another  body. 

Emily,  Therefore  a  small  body  may  have  a  great- 
er momentum  than  a  large  one,  provided  its  velocity 
be  sufficiently  greater  ;  for  instance,  the  momentum 
of  an  arrow  shot  from  a  bow  must  be  greater  than  a 
stone  thrown  by  the  hand. 

Caroline.  We  know  also  by  experience,  that  the 
heavier  a  body  is,  the  greater  is  its  force  ;  it  is  not 
therefore  difficult  to  understand,  that  the  whole  pow- 
er or  momentum  of  a  body  must  be  composed  of  these 
two  properties  :  but  I  do  not  understand  why  they 
should  be  multiplied  the  one  by  the  other ;  I  should 
have  supposed  that  the  quantity  of  matter  should  have 
been  added  to  the  quantity  of  motion  ? 

Mrs.  B.  It  is  found  by  experiment,  that  if  the 
weight  of  a  body  is  represented  by  the  number  3, 
and  its  velocity  also  by  3,  its  momentum  will  be  re- 
6 


50  ON  THE  LAWS  OP  MOTION, 

presented  by  9  ;  not  6,  as  would  be  the  case  were 
these  figures  added,  instead  of  being  multiplied  toge- 
ther. 1  recommend  it  to  you  to  be  careful  to  re- 
member the  definition  of  the  momentum  of  bodies,  as 
it  is  one  of  the  most  important  points  in  mechanics  ; 
you  will  find,  that  it  is  from  opposing  motion  to  mat- 
ter, that  machines  derive  their  powers.* 

The  reaction  of  bodies  is  the  next  law  of  motion 
which  I  must  explain  to  you.  When  a  body  in  mo- 
tion strikes  against  another  body,  it  meets  with  resist- 
ance from  it  ;  the  resistance  of  the  body  at  rest  will 
be  equal  to  the  blow  struck  by  the  body  in  motion  ; 
or,  to  express  myself  in  philosophical  language,  action 
and  re-action  wiW  be  equal,  and  in  opposite  directions. 

Caroline,  Do  you  mean  to  say,  that  the  action  of 
the  body  which  strikes  is  returned  with  equal  force 
by  the  body  which  receives  the  blow. 

Mrs.  B.     Exactly. 

Caroline.  But  if  a  man  strikes  another  on  the  face 
with  his  fist,  he  surely  does  not  receive  as  much  pain 
by  the  re-action  as  he  inflicts  by  the  blow  ? 

Mrs.  B.  No  ;  but  this  is  simply  owing  to  the 
knuckles  having  much  less  feeling  than  the  face. 

Here  are  two  ivory  balls  suspended  by  threads, 
(Plate  I.  fig.  3.)  draw  one  of  them,  A,  a  little  on  one 
side, — now  let  it  go  ; — it  strikes,  you  see,  against  the 
other  ball  B,  and  drives  it  off,  to  a  distance  equal  to 
that  through  which  the  first  ball  fell ;  but  the  motion 
of  A  is  stopped,  because  when  it  struck  B,  it  received 
in  return  a  blow  equal  to  that  it  gave,  and  its  motion 
was  consequently  destroyed. 


*  In  comparing  together  the  momenta  of  different  bodies,  we 
must  be  attentive  to  measure  their  weights  and  velocities,  by  the 
same  denomination  of  weights  and  of  spaces,  otherwise  the  re- 
sults would  not  agree.  Thus,  if  we  estimate  the  weight  of  one 
body  in  ounces,  we  must  estimate  the  weight  of  the  rest  also  in 
ounces,  and  not  in  pounds ;  and  in  computing  the  velocities,  in 
like  manner,  we  should  adhere  to  the  same  standard  of  measure, 
both  of  space  and  of  time;  as  for  instance,  the  number  of  feet 
in  one  second,  or  of  mile?  in  one  hour. 


ON  THE  LAWS  OF  MOTION.  51 

Emily.  I  should  have  supposed,  that  the  motion  of 
the  ball  A  was  destroyed,  because  it  had  communica- 
ted all  its  motion  to  B. 

Mrs.  B.  It  is  perfectly  true,  that  when  one  body 
strikes  against  another,  the  quantity  of  motion  com- 
municated to  the  second  body,  is  lost  by  the  first ;  but 
this  loss  proceeds  from  the  action  of  the  body  which 
is  struck. 

Here  are  six  ivory  halls  hanging  in  a  row, (fig.  4.) 
draw  the  first  out  of  the  perpendicular,  and  let  it  fall 
against  the  second.  None  of  the  balls  appear  to 
move,  you  see,  except  the  last,  which  flies  off  as  far 
as  the  first  ball  fell  ;  can  you  explain  this  ? 

Caroline.  I  believe  so.  When  the  first  ball 
struck  the  second,  it  received  a  blow  in  return, 
which  destroyed  its  motion  ;  the  second  ball,  though  it 
did  not  appear  to  move,  must  have  struck  against  the 
third  ;  the  re-action  of  which  set  it  at  rest ;  the  actioa 
of  the  third  ball  must  have  been  destroyed  by  the  re- 
action of  the  fourth,  and  so  on,  till  motion  was  com- 
municated to  the  last  ball,  which,  not  being  re-acted 
upon,  flies  off. 

Mrs.  B.  Very  well  explained.  Observe,  that  it 
is  only  when  bodies  are  elastic,  as  these  ivory  balls 
are,  that  the  stroke  returned  is  equal  to  the  stroke 
given.  I  will  show  you  the  difference  with  these 
two  balls  of  clay,  (fig.  5.)  which  are  not  elastic  ; 
when  you  raise  one  of  these,  D,  out  of  the  perpendi- 
cular, and  let  it  fall  against  the  other,  E,  the  re-action 
of  the  latter,  on  account  of  its  not  being  elastic,  is  not 
sufficient  to  destroy  the  motion  of  the  former ;  only 
part  of  the  motion  of  D  will  be  comolunicated  to  E, 
and  the  two  balls  will  move  on  together  to  d  and  e, 
which  is  not  to  so  great  a  distance  as  that  through 
which  D  fell. 

Observe  how  useful  re-action  is  in  nature.  Birds, 
in  flying,  strike  the  air  with  their  wings,  and  it  is  the 
re-action  of  the  air  which  enables  them  to  rise, 
or  advance  forw-ards  ;  re-action  being  always  in  a 
contrary  direction  to  action. 


d2  ON  THE  LAWS  OF  MOTION. 

Caroline,  I  thought  that  birds  might  be  lighter 
than  the  air  when  their  wings  were  expanded,  and 
\)y  that  means  enabled  to  fly. 

Mrs.  B.  When  their  wings  are  spread,  they  are 
better  supported  by  the  air,  as  they  cover  a  greater 
extent  of  surface  ;  but  they  are  still  much  too  heavy 
to  remain  in  that  situation,  without  continually  flap- 
ping their  wings,  as  you  may  have  noticed,  when 
birds  hover  over  their  nests  ;  the  force  with  which 
their  wings  strike  against  the  air  must  equal  the 
weight  of  their  bodies,  in  order  that  the  re-action  of 
the  air  may  be  able  to  support  that  weight ;  the  bird 
will  then  remain  stationary.  If  the  stroke  of  the 
wings  is  greater  than  is  required  merely  to  support 
the  bird,  the  re-action  of  the  air  will  make  it  rise  ;  if 
it  be  less,  it  will  gently  descend  ;  and  you  may  have 
observed  the  larlf,  sometimes  remaining  with  its 
wings  extended,  but  motionless  ;  in  this  state  it  drops 
rapidly  into  its  nest. 

Caroline,  What  a  beautiful  eflect  this  is  of  the  law 
of  re-action  !  But  if  flying  is  merely  a  mechanical 
operation,  Mrs.  B.,  why  should  we  not  construct 
wings,  adapted  to  the  size  of  our  bodies,  fasten  them 
to  our  shoulders,  move  them  with  our  arms,  and  soar 
into  the  air. 

Mrs.  B.  Such  an  experiment  has  been  repeatedly 
attempted,  but  never  with  success  ;  and  it  is  now 
considered  as  totally  impracticable.  The  muscular 
power  of  birds  is  greater  in  proportion  to  their  weight 
than  that  of  man  ;  were  we  therefore  furnished  with 
wings  sufficiently  large  to  enable  us  to  fly,  we  should 
not  have  strength  to  put  them  in  motion. 

In  swimming,  a  similar  action  is  produced  on  the 
water,  as  that  on  the  air  in  flying  :  and  also  in  rowing ; 
you  strike  the  water  with  the  oars,  in  a  direction  op- 
posite to  that  in  which  the  boat  is  required  to  move, 
and  it  is  the  re-action  of  the  water  on  the  oars 
which  drives  the  boat  along. 

Emily.     You  said,  that  it  was  in  elastic  bodies  only 


ON  THE  LAWS  OF  MOTION.  S3 

that  re-action  was  equal  to  action  ;  pray  what  bodies 
are  elastic  besides  the  air  ? 

Mrs,  B.  In  speaking  of  the  air,  I  think  we  defined 
elasticity  to  be  a  property,  by  means  of  which  bodies 
that  are  compressed  return  to  their  former  state,  if 
I  bend  this  cane,  as  soon  as  I  leave  it  at  liberty  it  re- 
covers its  former  position  ;  if  I  press  my  finger  upon 
your  arm,  as  soon  as  I  remove  it,  the  flesh,  by  virtue 
of  its  elasticity,  rises  and  destroys  the  impression  I 
made.  Of  all  bodies,  the  air  is  the  most  eminent  for 
this  property,  and* it  has  thence  obtained  the  name  of 
elastic  fluid.  Hard  bodies  are  in  tli€  next  degree 
elastic  ;  if  two  ivory,  or  metallic  balls  are  struck  to- 
gether, the  parts  at  which  they  touch  will  be  flatten- 
ed ;  but  their  elasticity  will  make  them  instantane- 
ously resume  their  former  shape. 

Caroline.  But  when  two  ivory  balls  strike  against 
each  other,  as  they  constantly  do  on  a  biUiard  table,  no 
mark  or  impression  is  made  by  the  stroke. 

Mrs,  B.  I  beg  your  pardon  ;  but  you  cannot  per^ 
ceive  any  mark,  because  their  elasticity  instantly  de- 
stroys all  trace  of  it. 

Soft  bodies,  which  easily  retain  impressions,  such 
as  clay,  wax,  tallow,  butter,  &c.  have  very  little  elas- 
ticity ;  but  of  all  descriptions  of  bodies  liquids  are  the 
least  elastic. 

Emily.  If  sealing-wax  were  elastic,  instead  of  re- 
taining the  impression  of  a  seal,  it  would  resume  a 
smooth  surface  as  soon  as  the  weight  of  the  seal  was 
removed.  But  pray  what  is  it  that  produces  the 
elasticity  of  bodies  ? 

Mrs.  B.  There  is  great  diversity  of  opinion  upon 
that  point,  and  I  cannot  pretend  to  decide  which  ap- 
proaches nearest  to  the  truth.  Elasticity  implies  sus- 
ceptibility of  compression,  and  the  susceptibility  of 
compression  depends  upon  the  porosity  of  bodies, 
for  were  there  no  pores  or  spaces  between  the  par- 
ticles of  matter  of  which  a  body  is  composed,  it  could 
not  be  compressed. 

Caroline,  That  is  to  say,  that  if  the  particles  of 
6* 


54  ox  THE  LAWS  OP  MOTION. 

bodies  were  as  close  together  as  possible,  they  could 
not  be  squeezed  closer. 

Emily.  Bodies  then,  whose  particles  are  most  dis- 
tant from  each  other,  must  be  most  susceptible  of 
compression,  and  consequently  most  elastic  ;  and  this 
you  say  is  the  case  with  air,  which  is  perhaps  the 
least  dense  of  all  bodies  ? 

Mrs.  B.  You  will  not  in  general  find  this  rule 
hold  good,  for  liquids  have  scarcely  any  elasticity, 
whilst  hard  bodies  are  eminent  for  this  property, 
though  the  latter  are  certainly  of  much  greater  den- 
sity than  the  former ;  elasticity  impHes,  therefore, 
not  only  a  susceptibility  of  compression,  but  depends 
upon  the  power  of  resuming  its  former  state  after 
compression. 

Caroline.  But  surely  there  can  be  no  pores  in 
ivory  and  metals,  Mrs.  B.  *  how  then  can  they  be 
Susceptible  of  compression  ? 

Mrs.  B.  The  pores  of  such  bodies  are  invisible  to 
the  naked  eye,  but  you  must  not  thence  conclude 
that  they  have  none  ;  it  is,  on  the  contrary,  well  as- 
certained that  gold,  one  of  the  most  dense  of  all  bo- 
die!^,  is  extromely  porous,  and  that  these  pores  are 
sufTiciently  large  to  admit  water  when  strongly  com- 
pressed to  pass  through  them.  This  was  shown  by 
a  f  -Jebrated  experiment  made  many  years  ago  at 
Florence. 

Emily.  If  water  can  pass  through  gold,  there 
must  certainly  be  pores  or  interstices  which  afford  it 
a  passage  ;  and  if  gold  is  so  porous,  what  must  other 
Ijodies  be,  which  are  so  much  less  dense  than  gold  ! 

Mrs.  B.  The  chief  difference  in  this  respect  is,  I 
believe,  that  the  pores  in  some  bodies  are  larger  thao 
in  others  ;  in  cork,  sponge,  and  bread,  they  form  con- 
liderable  cavities  ;  in  wood  and  stone,  when  not  po- 
lished, they  are  generally  perceptible  to  the  naked 
eye ;  whilst  in  ivory,  metals,  and  all  varnished  and 
polished  bodies,  they  cannot  be  discerned.  To  give 
you  an  idea  of  the  extreme  porosity  of  bodies,  Sir 
Isaac  Newtoa  conjectured  that  if  the  earth  were  so 


ON  THE  LAWS  OF  MOTIOfiT.  5# 

compressed  as  to  be  absolutely  without  pores,  its 
dimensions  might  possibly  not  be  more  than  a  cubic 
inch. 

Caroline,  What  an  idea !  Were  we  not  indebted 
to  Sir  Isaac  Newton  for  the  theory  of  attraction,  I 
should  be  tempted  to  laugh  at  him  for  such  a  supposi- 
tion. What  insigniticant  Httle  creatures  we  should  be  J 

Mrs.  B.  If  our  consequence  arose  from  the  size 
of  our  bodies  we  should  indeed  be  but  pigmies,  but 
remember  that  the  mind  of  Newton  was  not  circum- 
scribed by  the  dimensions  of  its  envelope. 

Emily.  It  is,  however,  fortunate  that  heat  keeps 
the  pores  of  matter  open  and  distended,  and  prevents 
the  attraction  of  cohesion  from  squeezing  us  into  a 
nutshell. 

Mrs.  B.  Let  us  now  return  to  the  subject  of  re- 
action, on  which  we  have  some  further  observations 
to  make.  It  is  re-action  being  contrary  to  action 
which  produces  reflected  motion,  if  you  throw  a  ball 
against  the  wall,  it  rebounds  ;  this  return  of  the  ball 
is  owing  to  the  re-action  of  the  wall  against  which  it 
struck,  and  is  called  reflected  motion. 

Emily.  And  I  now  understand  why  balls  filled  with 
air  rebound  better  than  those  stuffed  with  bran  or 
wool;  air  being  most  susceptible  of  compression  and 
most  elastic,  the  re-action  is  more  complete. 

Caroline.  I  have  observed  that  when  I  throw  a 
ball  straight  against  the  wall,  it  returns  straight  to  my 
hand ;  but  if  I  throw  it  obliquely  upwards,  it  rebounds 
still  higher,  and  I  catch  it  when  it  falls. 

Mrs.  B.  You  should  not  say  straight,  but  perpen- 
dicularly against  the  wall ;  for  straight  is  a  general 
term  for  lines  in  all  directions  which  are  neither 
curved  nor  bent,  and  is  therefore  equally  applicable 
to  oblique  or  perpendicular  lines. 

Caroline.  I  thought  that  perpendicularly  meant 
either  directly  upwards  or  downwards  ? 

Mrs.  B.  In  those  directions  lines  are  perpendicu- 
lar to  the  earth.  A  perpendicular  line  has  always  a 
reference  to  something  towards  which  it  is  perpen- 


56  ON  THE  LAWS  OF  MOTION. 

dicular ;  that  is  to  say,  that  it  inclines  neither  to  the 
one  side  or  the  other,  but  makes  an  equal  angle  on 
every  side.     Do  you  understand  what  an  angle  is  ? 

Caroline.  Yes,  I  believe  so  :  it  is  two  lines  meet- 
ing in  a  point. 

Mrs.  B.  Well  then,  let  the  line  A  B  (plate  II,  fig. 
1.)  represent  the  floor  of  the  room,  and  the  line  C  D 
that  in  which  you  throw  a  ball  against  it ;  the  line  C 
D,  you  will  observe,  forms  two  angles  with  the  line 
A  B,  and  those  two  angles  are  equal. 

Emily.  How  can  the  angles  be  equal,  while  the 
lines  which  compose  them  are  of  unequal  length  ? 

Mrs.  B.  An  angle  is  not  measured  by  the  length 
of  the  lines,  but  by  their  opening. 

Emily.  Yet  the  longer  the  lines  are,  the  greater 
is  the  opening  between  them. 

Mrs.  B.  Take  a  pair  of  compasses  and  draw  a  cir- 
cle  over  these  angles,  making  the  angular  point  the 
centre. 

Emily.  To  what  extent  must  I  open  the  com- 
passes ? 

Mrs.  B.  You  may  draw  the  circle  what  size  you 
please,  provided  that  its  cuts  the  lines  of  the  angles 
we  are  to  measure.  All  circles,  of  whatever  dimen- 
sions, are  supposed  to  be  divided  into  360  equal  parts, 
called  degrees  ;  the  opening  of  an  angle,  being  there- 
fore a  portion  of  a  circle,  must  contain  a  certain  num- 
ber of  degrees  ;  the  larger  the  angle,  the  greater  the 
number  of  degrees,  and  two  angles  are  said  to  be 
»cqual  when  they  contain  an  equal  number  of  degrees. 

Emily.  Now  1  understand  it.  As  the  dimensions 
of  an  angle  depend  upon  the  number  of  degrees  con- 
tained between  its  lines,  it  is  the  opening,  and  not  the 
length  of  its  lines,  which  determines  the  size  of  the 
angle. 

Mrs.  B.  Very  well :  now  that  you  have  a  clear 
idea  of  the  dimensions  of  angles,  can  you  tell  me  how 
many  degrees  are  contained  in  the  two  angles  formed 
by  one  line  falling  perpendicularly  on  another,  as  in 
the  figure  1  have  just  drawn  ? 


PLATE    n. 


n 


» 


ON  THE  LAWS  OF  MOTION.  61 

Emily.  You  must  allow  me  to  put  one  foot  ol* 
the  compasses  at  the  point  of  the  angles,  and  draw  a 
circle  round  them,  and  then  I  think  1  shall  be  able  to 
answer  your  question  :  the  two  angles  are  together 
just  equal  to  half  a  circle,  they  contain  therefore  90 
degrees  each  ;  90  degrees  being  a  quarter  of  360. 

Mrs.  B.  An  angle  of  90  degrees  is  called  a  right 
angle,  and  when  one  line  is  perpendicular  to  another, 
it  forms,  you  see,  (fig.  1.)  a  right  angle  on  either 
side.  Angles  containing  more  than  90  degrees  are 
called  obtuse  angles  ;  (fig.  2.)  and  those  containing 
less  than  90  degrees  are  called  acute  angles,  (fig.  3.) 

Caroline.  The  angles  of  this  square  table  are  right 
angles,  but  those  of  the  octagon  table  are  obtuse  an- 
gles ;  and  the  angles  of  sharp-pointed  instruments  are 
acute  angles. 

Mrs.  B.  Very  well.  To  retarn  now  to  your  ob- 
servation, that  if  a  ball  is  thrown  obliquely  against 
the  wall  it  will  not  rebound  in  the  same  direction ; 
tell  me,  have  you  ever  played  at  billiards  ? 

Caroline,  Yes,  frequently  ;  and  I  have  observed 
that  when  I  push  the  ball  perpendicularly  against  the 
cushion,  it  returns  in  the  same  direction  ;  but  when 
I  send  it  obliquely  to  the  cushion,  it  rebounds  ob- 
liquely, but  on  the  opposite  side  ;  the  ball  in  this  lat- 
ter case  describes  an  angle,  the  point  of  which  is  at 
the  cushion.  I  have  observed  too,  that  the  more  ob- 
liquely the  ball  is  struck  against  the  cushion,  the 
more  obliquely  it  rebounds  on  the  opposite  side,  so 
that  a  billiard  player  can  calculate  with  great  accu- 
racy in  what  direction  it  will  return. 

Mrs.  B.  Very  well.  This  figure  (fig.  4.  plate  II.) 
represents  a  billiard  table  ;  now  if  you  draw  a  line 
A  B  from  the  point  where  the  ball  A  strikes  perpen- 
dicular to  the  cushion  ;  you  will  find  that  it  will  di- 
vide the  angle  which  the  ball  describes  into  two  parts, 
or  two  angles  ;  the  one  will  show  the  obliquity  of  the 
direction  of  the  ball  in  its  passage  towards  the  cush- 
ion, the  other  its  obliquity  in  its  passage  back  from 
the  cushion.     The  first  is  called  the  angle  of  inci- 


58  ON  THE  LAWS  OF  MOTION. 

dence^  the  other  the  angle  of  reflection,  and  these  ao- 
gles  are  always  equal. 

Caroline.  This  then  is  the  reason  why,  when  I 
throw  a  ball  obliquely  against  the  wall,  it  rebounds  in 
an  opposite  oblique  direction,  forming  equal  angles  of 
incidence  and  of  reflection. 

Mrs,  B.  Certainly  ;  and  you  will  find  that  the 
more  obliquely  you  throw  the  ball,  the  more  oblique- 
ly it  will  rebound. 

We  must  now  conclude  ;  but  I  shall  have  some 
further  observations  to  make  upon  the  laws  of  mo- 
tion, at  our  next  meeting. 


CONVERSATION  IV. 


ON  COxMPOUND  MOTION. 

Compound  Motion,  the  Result  of  two  Opposite  For- 
ces.— Of  Circular  Motion,  the  Result  of  two  Forces, 
one  of  which  confines  the  Body  to  a  Fixed  Point. — 
Centre  of  Motion,  the  Point  at  Rest  while  the  other 
Parts  of  the  Body  move  round  it. — Centre  of  Magni- 
tude, the  Middle  of  a  Body. — Centripetal  Force,  that 
which  confines  a  Body  to  a  fixed  Central  Point. — 
Centrifugal  Force,  that  which  impels  a  Body  to  fly 
from  the  Centre. — Fall  of  Bodies  in  a  Parabola. — 
Centre  of  Gravity,  the  Centre  of  Weight,  or  point 
about  which  the  Parts  balance  each  other, 

MRS.  B.  I  must  explain  to  you  the  nature  of  com- 
pound motion.  Let  us  suppose  a  body  to  be  struck 
by  two  equal  forces  in  opposite  directions,  how  will 
it  move  ? 

Emily.  If  the  directions  of  the  forces  are  in  exact 
opposition  to  each  other,  I  suppose  the  body  would 
not  move  at  all. 

Mrs.  B.  You  are  perfectly  right ;  but  if  the  for- 
ces, instead  of  acting  on  the  body  in  opposition,  strike 
it  in  two  directions  inclined  to  each  other,  at  an  angle 
of  ninety  degrees,  if  the  ball  A  (fig.  6.  plate  II.)  be 
struck  by  equal  forces  at  X  and  at  Y,  will  it  not 
move  ? 

Emily.  The  force  X  would  send  it  towards  ,B,  and 
the  force  Y  towards  C  ;  and  since  these  forces  are 
equal,  I  do  not  know  how  the  body  can  obey  one  im^ 
pulse  rather  than  the  other,  and  yet  I  think  the  ball 


60  ON  COMPOUND  MOTION. 

would  move,  because,  as  the  two  forces  do  not  act  in 
direct  opposition,  they  cannot  entirely  destroy  the 
effect  of  each  other. 

Mrs,  B,  Very  true  ;  the  ball  will  therefore  follow 
the  direction  of  neither  of  the  forces,  but  will  move 
in  a  line  between  them,  and  will  reach  D  in  the  same 
space  of  time,  that  the  force  X  would  have  sent  it  to 
B,  and  the  force  Y  would  have  sent  it  to  C.  Now,  if 
you  draw  two  lines  from  D,  to  join  B  and^,  you  will 
form  a  square,  and  the  oblique  line  which  the  body 
describes  is  called  the  diagonal  of  the  square. 

Caroline.  That  is  very  clear,  but  supposing  the 
two  forces  to  be  unequal,  that  the  force  X,  for  in* 
stance,  be  twice  as  great  as  the  force  Y  ? 

Mrs.  B.  Then  the  force  X  would  drive  the  ball 
twice  as  far  as  the  force  Y,  consequently  you  must 
draw  the  line  A  B  (fig.  6.)  twice  as  long  as  the  line 
A  C,  the  body  will  in  this  case  move  to  D  ;  and  if 
you  draw  lines  from  that  point  to  B  rand  C,  you  will 
iind  that  the  ball  has  moved  in  the  diagonal  of  a 
rectangle. 

Emily.  Allow  me  to  put  another  case  ?  Suppose 
the  two  forces  are  unequal,  but  do  not  act  on  the  ball 
in  the  direction  of  a  right  angle,  'but  in  that  of  an 
acute  angle,  what  will  result  ? 

Mrs.  B.  Prolong  the  lines  in  the  directions  of  the 
two  forces,  and  you  will  soon  discover  which  way  the 
ball  will  be  impelled  ;  it  will  move  from  A  to  D,  in  the 
diagonal  of  a  parallelogram,  (fig.  7.)  Forces  acting 
in  the  direction  of  lines  forming  an  obtuse  angle,  will 
also  produce  motion  in  the  diagonal  of  a  parallel- 
ogram. For  instance,  if  the  body  set  out  from  B, 
instead  of  A,  and  was  impelled  by  the  forces  X  and 
Y,  it  would  move  in  the  dotted  diagonal  B  C. 

We  may  now  proceed  to  circular  motion :  this  is 
the  result  of  two  forces  on  a  body,  by  one  of  which 
it  is  projected  forward  in  a  right  line,  whilst  by  the 
other  it  is  confined  to  a  fixed  point.  For  instance, 
when  1  whirl  this  ball,  which  is  fastened  to  ray  hand 
with  a  string,  the  ball  moves  in  a  circular  direction  ; 


ON  COMPOUND  MOTION.  01 

because  it  is  acted  on  by  two  forces,  that  which  I 
give  it,  which  represents  the  force  of  projection,  and 
that  of  the  string,  which  confines  it  to  my  hand.  If 
during  its  motion  you  were  suddenly  to  cut  the  string, 
the  ball  would  fly  off  in  a  straight  line  ;  being  releas- 
ed from  confinement  to  the  fixed  point,  it  would  be 
acted  on  but  by  one  force,  and  motion  produced  by 
one  force,  you  know,  is  always  in  a  right  hne. 

Caroline.  This  is  a  little  more  difficult  to  compre- 
hend than  compound  motion  in  straight  hnes. 

Mrs.  B.  You  have  seen  a  mop  trundled,  and  have 
observed  that  the  threads  which  compose  the  head 
-of  the  mop  fly  from  the  centre  ;  but  being  confined 
to  it  at  one  end,  they  cannot  part  from  it ;  whilst  the 
water  they  contain,  being  unconfined,  is  thrown  off  in 
straight  lines. 

Emily.  In  the  same  way,  the  flyers  of  a  windmill, 
when  put  in  motion  by  the  wind,  would  be  driven 
straight  forwards  in  a  right  line,  were  they  not  con- 
fined to  a  fixed  point,  round  which  they  are  compel- 
led to  move. 

Mrs.  B.  Very  well.  And  observe,  that  the  point 
to  which  the  motion  of  a  small  body,  such  as  the  ball 
with  the  string,  which  may  be  considered  as  revolv- 
ing in  one  plane,  is  confined,  becomes  the  centre  of 
its  motion.  But  when  the  bodies  are  not  of  a  size  or 
shape  to  allow  of  our  considering  every  part  of  them 
as  moving  in  the  same  plane,  they  in  reality  revolvje 
round  a  line,  which  line  is  called  the  axis  of  motion. 
In  a  top,  for  instance,  when  spinning  on  its  point,  the 
axis  is  the  line  which  passes  through  the  middle  of  it, 
perpendicularly  to  the  floor. 

Caroline.  The  axle  of  the  flyers  of  the  windmill 
is  then  the  axis  of  its  motion  ;  but  is  the  centre  of 
motion  always  in  the  middle  of  a  body  ? 

Mrs.  B.  No,  not  always.  The  middle  point  of  a 
body  is  called  its  centre  of  magnitude,  or  position, 
that  is,  the  centre  of  its  mass  or  bulk.  Bodies  have 
also  another  centre,  called  the  centre  of  gravity, 
»y}iich  I  shall  explain  to  you  ;  but  at  present,  we  must 


62  ON  COMPOUND  MOTION. 

confine  ourselves  to  the  axis  of  motion.  This  line 
you  must  observe  remains  at  rest,  whilst  all  the  other 
parts  of  the  body  move  around  it ;  when  you  spin  a 
top  the  axis  is  stationary  whilst  every  other  part  is  in 
motion  round  it. 

Caroline.  But  a  top  generally  has  a  motion  for- 
wards, besides  its  spinning  motion ;  and  then  no  point 
within  it  can  be  at  rest  ? 

Mrs.  B.  What  i  say  of  the  axis  of  motion,  relates 
only  to  circular  motion  ;  that  is  to  say,  to  motion 
round  a  line,  and  not  to  that  which  a  body  may  have 
at  the  same  time  in  any  other  direction.  There  is 
one  circumstance  in  circular  motion,  which  you  must 
carefully  attend  to  ;  which  is,  that  the  further  any 
part  of  a  body  is  from  the  axis  of  motion,  the  greater 
is  its  velocity  ;  as  you  approach  that  line,  the  velo- 
city of  the  parts  gradually  diminishes  till  you  reach  the 
axis  of  motion,  which  is  perfectly  at  rest. 

Caroline.  But,  if  every  part  of  the  same  body  did 
not  move  with  the  same  velocity,  that  part  which 
moved  quickest  must  be  separated  from  the  rest  of 
the  body,  and  leave  it  behind  ?  ^ 

Mrs.  B.  You  perplexyourself  by  confounding  the 
idea  of  circular  motion  with  that  of  motion  in  a  right 
line  :  you  must  think  only  of  the  motion  of  a  body 
round  a  fixed  line,  and  you  will  find,  that  if  the  parts 
farthest  from  the  centre  had  not  the  greatest  velocity, 
those  parts  would  not  be  able  to  keep  up  with  the 
rest  of  the  body,  and  would  be  left  behind.  Do  not 
the  extremities  of  the  vanes  of  a  windmill  move  over 
a  much  greater  space,  than  the  parts  nearest  the  axis 
of  motion  ?  (plate  III.  fig.  1.)  the  three  dotted  circles 
describe  the  paths  in  which  three  different  parts  of 
the  vanes  move,  and  though  the  circles  are  of  diff'er- 
ent  dimensions,  the  vanes  describe  each  of  them  in 
the  same  space  of  time. 

Caroline.  Certainly  they  do  ;  and  I  now  only  won- 
der, that  we  neither  of  us  ever  made  the  observation 
before  :  and  the  same  effect  must  take  place  in  a  so- 
lid body,  like  the  top,  in  spinning ;  the  most  bulging 


%■  ^■ 


PLATE  n 


Fi^S. 


Fi^.4 


%•  '^■ 


Fi^.  S. 


F^  8 


ON  COxMPOUND  MOTION.  63 

part  of  the  surface  must  move  with  the  greatest  rapi- 

dfty. 

Mrs.  B.  The  force  which  confines  a  body  to  a 
centre  round  which  it  moves  is  called  the  centripetal 
force  ;  and  that  force,  which  impels  a  body  to  fly 
from  the  centre,  is  called  the  centrifugal  force  ;  in 
circular  motion,  these  two  forces  constantly  balance 
each  other  :  otherwise  the  revolving  body  would  ei- 
ther approach  the  centre,  or  recede  from  it,  accord- 
ing as  the  one  or  the  other  prevailed. 

Caroline.  When  I  see  any  body  moving  in  a  circle, 
I  shall  remember  that  it  is  acted  on  by  two  forces. 

Mrs.  B.  Motion,  either  in  a  circle,  an  ellipsis,  or 
any  other  curve-line,  must  be  the  result  of  the  action 
of  two  forces  ;  for  you  know,  that  the  impulse  of  one 
single  force  always  produces  motion  in  a  right  line. 

Emily.  And  if  any  cause  should  destroy  the  cen- 
tripetal force,  the  centrifugal  force  would  alone  im- 
pel the  body,  and  it  would  I  suppose  fly  off  in  a 
straight  line  from  the  centre  to  which  it  had  been 
confined. 

Mrs.  B.  It  would  not  fly  off"  in  a  right  line  from 
the  centre  ;  but  in  a  right  line  in  the  direction  in 
which  it  was  moving,  at  the  instant  of  its  release  ;  if  a 
stone,  whirled  round  in  a  sling,  gets  loose  at  the 
point  A,  (plate  III.  fig.  2.)  it  flies  off  in  the  direction 
A  B  ;  this  Hne  is  called  a  tangent,  it  touches  the  cir- 
cumference of  the  circle,  and  forms  a  right  angle 
with  a  line  drawn  from  that  point  of  the  circumfer- 
ence to  the  centre  of  the  circle,  C. 

Emily.  You  say,  that  motion  in  a  curve-line  is 
owing  to  two  forces  acting  upon  a  body  ;  but  when  1 
throw  this  ball  in  a  horizontal  direction,  it  describes 
a  curve-line  in  falling  ;  and  yet  it  is  only  acted  upon 
by  the  force  of  projection  ;  there  is  no  centripetal 
force  to  confine  it,  or  produce  compound  motion. 

Mrs.  B.  A  ball  thus  thrown,  is  acted  upon  by  no 
less  than  three  forces  ;  the  force  of  projection,  which 
you  communicated  to  it ;  the  resistance  of  the  air 
through  which  it  passes,  which  diminishes  its  veloci- 


04  ON  COMPOUND  MOTION. 

ty,  without  changing  its  direction  ;  and  the  force  of 
gravit}^  which  finally  brings  it  to  the  ground.  The 
power  of  gravity,  and  the  resistance  of  the  air,  being 
always  greater  than  any  force  of  projection  we  can 
give  a  body,  the  lattdr  is  gradually  overcome,  and  the 
body  brought  to  the  ground  ;  but  the  stronger  the 
projectile  force,  the  longer  will  these  powers  be  in 
subduing  it,  and  the  further  the  body  will  go  before  it 
falls. 

Caroline.  A  shot  fired  from  a  cannon,  for  instance, 
will  go  much  further  than  a  stone  projected  by  the 
hand. 

Mrs.  B.      Bodies   thus   projected,  you  observed, 
described  a  curve-line  in  their  descent;  can  you  ac- 
' count  for  that? 

Caroline.  No ;  I  do  not  understand  why  it  should 
not  fall  in  the  diagonal  of  a  square. 

Mrs.  B.  You  must  consider  that  the  force  of  pro- 
jection is  strongest  when  the  ball  is  first  thrown  ;  this 
force,  as  it  proceeds,  being  weakened  by  the  continued 
resistance  of  the  air,  the  stone,  therefore,  begins  by 
moving  in  a  horizontal  direction  ;  but  as  the  strong- 
er powers  prevail,  the  direction  of  the  ball  will  gradu- 
ally change  from  a  horizontal  to  a  perpendicular 
line.  Projection  alone,  would  drive  the  ball  A,  to  B, 
(fig.  3.)  gravity  would  bring  it  to  C  ;  therefore,  when 
acted  on  in  different  directions,  by  these  two  forces, 
it  moves  between,  gradually  inclining  more  and  more 
to  the  force  of  gravity,  in  proportion  as  this  accumu- 
lates ;  instead  therefore  of  reaching  the  ground  at  D, 
as  you  supposed  it  would,  it  falls  somewhere  about  E. 

Caroline.  It  is  precisely  so  ;  look,  Emily,  as  I 
throw  this  ball  directly  upwards,  how  the  resistance 
of  the  air  and  gravity  conquers  projection.  Now  I 
will  throw  it  upwards  obliquely  ;  see,  the  force  of 
projection  enables  it,  for  an  instant,  to  act  in  opposi- 
tion to  that  of  gravity  ;  but  it  is  soon  brought  down 
again. 

Mrs.  B.  The  curve-line  which  the  ball  has  de- 
scribed, is  called  in  geometry  r  parabola  ;  but  when 


ON  COMPOUND  MOTION.  Qo 

the  ball  is  thrown  perpendicularly  upwards,  it  will 
descend  perpendicularly  ;  because  the  force  of  pro- 
jection, and  that  of  gravity,  are  in  the  same  line  of 
direction. 

We  have  noticed  the  centres  of  magnitude,  and  of 
motion  ;  but  I  have  not  yet  explained  to  you  what  is 
meant  by  the  centre  of  gravity  ;  it  is  that  point  in  a 
body,  about  which  all  the  parts  exactly  balance  each 
other  ;  if  therefore  that  point  is  supported,  the  body 
will  not  fall.     Do  you  understand  this  ? 

Emily.  I  think  so,  if  the  parts  round  about  this 
point  have  an  equal  tendency  to  fall,  they  will  be  in 
equilibrium,  and  as  long  as  this  point  is  supported, 
the  body  cannot  fall. 

Mrs.  B.  Caroline,  what  would  be  the  effect,  were 
any  other  point  of  the  body  alone  supported  ? 

Caroline.  The  surrounding  parts  no  longer  balan- 
cing each  other,  the  body,  I  suppose,  would  fall  on 
the  side  at  which  the  parts  are  heaviest. 

Mrs.  B.  Infallibly;  whenever  the  centre  ofgra 
vity  is  unsupported  the  body  must  fall.  This  some- 
times happens  with  an  overloaded  wagon  winding  up 
a  steep  hill,  one  side  of  the  road  being  more  elevated 
than  the  other ;  let  us  suppose  it  to  slope  as  is  de- 
scribed in  this  figure,  (plate  III.  fig.  4.,)  we  will  say, 
that  the  centre  of  gravity  of  this  loaded  wagon  is  at 
the  point  A.  Now  your  eye  will  tell  you,  that  a  wa- 
gon thus  situated  will  overset ;  and  the  reason  is, 
that  the  centre  of  gravity  A,  is  not  supported  ;  for  if 
you  draw  a  perpendicular  line  from  it  to  the  ground 
at  C,  it  does  not  fall  under  the  wagon  within  the 
wheels,  and  is  therefore  not  supported  by  them. 

Caroline.  I  understand  that  perfectly  ;  but  what 
is  the  meaning  of  the  other  point  B  ? 

Mre.  B.  Let  us,  in  imagination,  take  off  the  upper 
part  of  the  load  ;  the  centre  of  gravity  will  then 
change  its  situation,  and  descend  to  B,  as  that  will 
now  be  the  point  about  which  the  parts  of  the  less 
heavily  laden  wagon  will  balance  each  other.  Will 
the  wagon  now  be  upset? 

6* 


G.6  ON  COMPOUND  MOTION. 

Caroline.  No,  because  a  perpendicular  line  from 
that  point  falls  within  the  wheels  at  D,  and  is  support- 
ed by  them  ;  and  when  the  centre  of  gravity  is  sup- 
ported, the  body  will  not  fall. 

Emily,  Yet  I  should  not  much  like  to  pass  a  wa- 
gon in  that  situation  ;  for,  as  you  see,  the  point  D  is 
but  just  within  the  left  wheel ;  if  the  right  wheel  was 
merely  raised,  by  passing  over  a  stone,  the  point  D 
would  be  thrown  on  the  outside  of  the  left  wheel,  and 
the  wagon  would  upset. 

Caroline.  A  wagon,  or  any  carriage  whatever, 
will  then  be  most  firmly  supported,  when  the  centre 
of  gravity  falls  exactly  between  the  wheels  ;  and  that 
is  the  case  in  a  level  road. 

Pray,  whereabouts  is  the  centre  of  gravity  of  the 
human  body  ? 

Mrs.  B.  Between  the  hips  ;  and  as  long  as  we 
Stand  upright,  this  point  is  supported  by  the  feet ;  if 
you  lean  on  one  side,  you  will  find  that  you  no  longer 
stand  firm.  A  rope-dancer  performs  all  his  feats  of 
agility,  by  dexterously  supporting  his  centre  of  gravi- 
ty ;  whenever  he  finds  that  he  is  in  danger  of 
losing  his  balance,  he  shifts  the  heavy  pole,  which  be 
holds  in  his  hands,  in  order  to  throw  the  weight 
towards  the  side  that  is  deficient ;  and  thus,  by  chang- 
ing the  situation  of  the  centre  of  gravity,  he  restores 
his  equilibrium. 

Caroline.  When  a  stick  is  poised  on  the  tip  of  the 
finger,  is  it  not  by  supporting  its  centre  of  gravity  ? 

Mrs.  B.  Yes  ;  and  it  is  because  the  centre  of  gra- 
vity is  not  supported  that  spherical  bodies  roll  down 
aslope.  A  sphere,  being  perfectly  round,  can  touch 
the  slope  but  by  a  single  point,  and  that  point  cannot 
be  perpendicularly  under  the  centre  of  gravity,  and 
therefore  cannot  be  supported,  as  you  will  perceive 
by  examining  this  figure.  (Fig.  5.  plate  III.) 

Emily.  So  it  appears  ;  yet  I  have  seen  a  cylinder 
of  wood  roll  up  a  slope  ;  how  is  that  contrived  ? 

Mrs.  B.  It  is  done  by  plugging  one  side  of  the 
i^y Under  with  lead,  as  at  B,  (fig.  5»  plate  III.)  the  bo- 


ON  COMPOUND  MOTION.  6? 

dy  being  no  longer  of  a  uniform  density,  the  centre  of 
gravity  is  removed  from  the  middle  of  the  body  to 
some  point  in  the  lead,  as  that  substance  is  much  hea- 
vier than  wo«d  ;  now  you  may  observe  that  in  order 
that  the  cylinder  may  roll  down  the  plane,  as  it  is 
here  situated,  the  centre  of  gravity  must  rise,  which 
is  impossible  ;  the  centre  of  gravity  must  always  de- 
scend in  moving,  and  will  descend  by  the  nearest  and 
readiest  means,  which  will  be  by  forcing  the  cylinder 
up  the  slope,  until  the  centre  of  gravity  is  supported, 
and  then  it  stops. 

Caroline.  The  centre  of  gravity,  therefore,  is  not 
always  in  the  middle  of  a  body  ? 

Mrs.  B.  No,  that  point  we  have  called  the  centre 
of  magnitude;  when  the  body  is  of  a  uniform  densi- 
ty, the  centre  of  gravity  is  in  the  same  point;  but 
when  one  part  of  the  body  is  composed  of  heavier 
materials  than  another  part,  the  centre  of  gravity  be- 
ing the  centre  of  the  weight  of  the  body  can  no  long- 
er correspond  with  the  centre  of  magnitude.  Thus 
you  see  the  centre  of  gravity  of  this  cylinder  plugged 
with  lead,  cannot  be  in  the  same  spot  as  the  centre  of 
magnitude. 

Emily.  Bodies,  therefore,  consisting  but  of  one 
kind  of  substance,  as  wood,  stone,  or  lead,  and  whose 
densities  are  consequently  uniform,  must  stand  more 
firmly,  and  be  more  difficult  to  overset,  than  bodies 
composed  of  a  variety  of  substances^  of  different  den- 
sities, which  may  throw  the  centre  of  gravity  on  one 
side. 

Mrs.  B.  Yes ;  but  there  is  another  circumstance 
which  more  materially  affects  the  firmness  of  their 
position,  and  that  is  their  form.  Bodies  that  have  a 
narrow  base  are  easily  upset,  for  if  they  are  the  least 
inclined,  their  centre  is  no  longer  supported,  as  you 
may  perceive  in  fig.  6. 

Caroline.  I  have  often  observed  with  what  diffi- 
culty a  person  carries  a  single  pail  of  water  ;  it  is 
owing,  I  suppose,  to  the  centre  of  gravity  being 
thrown  on  one  side,  and  the  opposite  arm  is  stretched 


68  ON  COMPOUND  MOTION. 

out  to  endeavour  to  bring  it  back  to  it3  original  situa- 
tion  ;  but  a  pail  hanging  on  each  arm  is  carried  with- 
out difficulty,  because  they  balance  each  other,  and 
the  centre  of  gravity  remains  supported  by  the  feet. 

Mrs.  B.  Very  well ;  1  have  but  one  more  remark 
to  make  on  the  centre  of  gravity,  which  is,  that  when 
two  bodies  are  fastened  together,  by  a  line,  string, 
chain,  or  any  power  whatever,  they  are  to  be  consi- 
dered as  forming  but  one  body  ;  if  the  two  bodies  be 
of  equal  weight,  the  centre  of  gravity  will  be  in  the 
middle  of  the  line  which  unites  them,  (fig.  7.)  but  if 
one  be  heavier  than  the  other,  the  centre  of  gravity 
will  be  proportionally  nearer  the  heavy  body  than  the 
light  one.  (fig.  8.)  If  you  were  to  carry  a  rod  or 
pole  with  an  equal  weight  fastened  at  each  end  of  it, 
you  would  hold  it  in  the  middle  of  the  rod,  in  order 
that  the  weights  should  balance  each  other  ;  whilst  if 
it  had  unequal  weights  at  each  end,  you  would  hold 
it  nearest  the  greater  weight,  to  make  them  balance 
each  other. 

Emily.  And  in  both  cases  we  should  support  the 
centre  of  gravity  ;  and  if  one  weight  be  very  consi- 
derably larger  than  the  other,  the  centre  of  gravity 
will  be  thrown  out  of  the  rod  into  the  heaviest  weight. 
(fig.  9.) 

Mrs.  B.     Undoubtedlv. 


CONVERSATION  V. 


ON  THE  MECHANICAL  POWERS. 

Of  the  Power  of  Machines. — Of  the  Lever  in  General. 
— Of  the  Lever  of  the  First  Kind,  having  the  Fulcrum 
between  the  Power  and  the  Weight. — Of  the  Lever  of 
the  Second  Kind,  having  the  Weight  between  the  Pow- 
er and  the  Fulcrum. — Of  the  Lever  of  the  Third  Kindy 
having  the  Power  between  the  Fulcrum  and  the 
Weight. 

MRS.  B.  We  may  now  proceed  to  examine  the 
mechanical  powers ;  they  are  six  in  number,  one  or 
more  of  which  enters  into  the  composition  of  every 
machine.  The  lever,  the  pulley,  the  wheel,  and  axle^ 
the  inclined  plane,  the  wedge,  and  the  screw. 

In  order  to  understand  the  power  of  a  machine, 
there  are  four  things  to  be  considered.  1st.  The 
power  that  acts  :  this  consists  in  the  effort  of  men  or 
horses,  of  weights,  springs,  steam,  &c. 

2dly.  The  resistance  which  is  to  be  overcome  by 
the  power  ;  this  is  generally  a  weight  to  be  moved. 
The  power  must  always  be  superior  to  the  resist- 
ance, otherwise  the  machine  could  not  be  put  in  mo- 
tion. 

Caroline.  If  for  instance  the  resistance  of  a  car- 
riage was  greater  than  the  strength  of  the  horses 
employed  to  draw  it,  they  would  not  be  able  to  make 
it  move. 

Mrs,  B,  3dly.  We  are  to  consider  the  centre  of  mo~ 


TO        ON  THE  MECHANICAL  POWERS. 

tion,  or,  as  it  is  termed  in  mechanics,  the  fulcrum; 
this  you  may  recollect  is  the  point  about  which  all 
the  parts  of  the  body  move;  and,  lastly,  the  respective 
velocities  of  the  power,  and  of  the  resistance. 

Emily.  That  must  depend  upon  their  respective 
distances  from  the  axis  of  motion  ;  as  we  observed  in 
the  motion  of  the  vanes  of  the  windmill. 

Mrs.  B.  We  shall  now  examine  the  power  of  the 
lever.  The  lever  is  an  inflexible  rod  or  beam  of  any 
kind,  that  is  to  say,  one  which  will  not  bend  in  any 
direction.  For  instance,  the  steel  rod  to  which  these 
scales  are  suspended  is  a  lever,  and  the  point  in 
which  it  is  supported  the  fulcrum,  or  centre  of  mo- 
tion ;  now,  can  you  tell  me  why  the  two  scales  are 
in  equilibrium  ? 

Caroline.  Being  both  empty,  and  of  the  same 
weight,  they  balance  each  other. 

Emily.  Or,  more  correctly  speaking,  because  the 
centre  of  gravity  common  to  both  is  supported. 

Mrs.  B.  Very  well ;  and  which  is  the  centre  of 
gravity  of  this  pair  of  scales  ?  (fig.  1.  plate  III.) 

Emily.  You  have  told  us  that  when  two  bodies  of 
equal  weight  were  fastened  together,  the  centre  of 
gravity  was  in  the  middle  of  the  line  that  connected 
them  ;  the  centre  of  gravity  of  the  scales  must  there- 
fore be  in  the  fulcrum  F  of  the  lever  which  unites 
the  two  scales  ;  and  corresponds  with  the  centre  of 
motion. 

Caroline.  But  if  the  scales  contained  different 
weights,  the  centre  of  gravity  would  no  longer  be  in 
the  fulcrum  of  the  lever,  but  removed  towards  that 
scale  which  contained  the  heaviest  weight ;  and  since 
that  point  would  no  longer  be  supported,  the  heavy 
scale  would  descend  and  outweigh  the  other. 

Mrs.  B.  True  ;  but  tell  me,  can  you  imagine  any 
mode  by  which  bodies  of  different  weights  can  be 
made  to  balance  each  other,  either  in  a  pair  of  scales, 
or  simply  suspended  to  the  extremities  of  the  lever  ? 
for  the  scales  are  not  an  essential  part  of  the  machine, 
they  have  no  mechanical  power,  and  are  used  merely 


PLATu  nr 


ON  THE  MECHANICAL  POWERS.        71 

for  the  convenience  of  containing  the  substance  to 
be  weighed. 

Caroline.  What!  make  a  light  body  balance  a 
heavy  one  ?  I  cannot  conceive  that  possible. 

Mrs.  B.  The  fulcrum  of  this  pair  of  scales  (fig. 
2.)  is  moveable,  you  see  ;  I  can  take  it  ofif  the  prop, 
and  fiisten  it  on  again  in  another  part ;  this  part  is 
now  become  the  fulcrum,  but  it  is  no  longer  in  the 
centre  of  the  lever. 

Caroline.  And  the  scales  are  no  longer  true  ;  for 
that  which  hangs  on  the  longest  side  of  the  lever  de- 
scends. 

Mrs.  B.  The  two  parts  of  the  lever  divided  by 
the  fulcrum  are  called  its  arms,  you  should  therefore 
say  the  longest  arm,  not  the  longest  side  of  the  lever. 
These  arms  are  likewise  frequently  distinguished 
by  the  appellations  of  the  acting  and  the  resisting 
part  of  the  lever. 

Your  observation  is  true  that  the  balance  is  now 
destroyed  ;  but  it  will  answer  the  purpose  of  en- 
abling you  to  comprehend  the  power  of  a  lever  when 
the  fulcrum  is  not  in  the  centre. 

Emily.  This  would  be  an  excellent  contrivance 
for  those  who  cheat  in  the  weight  of  their  goods  ;  by 
making  the  fulcrum  a  little  on  one  side,  and  placing  the 
goods  in  the  scale  which  is  suspended  to  the  longest 
arm  of  the  lever,  they  would  4ippear  to  weigh  more 
than  they  do  in  reality. 

Mrs.  B.  You  do  not  consider  how  easily  the  fraud 
would  be  detected  ;  for  on  the  scales  being  emptied 
they  would  not  hang  in  equilibrium. 

Emily.  True  ;  I  did  not  think  of  that  circum- 
stance. But  I  do  not  understand  why  the  longest  arm 
of  the  lever  should  not  be  in  equilibrium  with  the 
other  ? 

Caroline.  It  is  because  it  is  heavier  than  the  short- 
est arm  ;  the  centre  of  gravity,  therefore,  is  no  long- 
er supported. 

Mrs.  B.  You  are  right ;  the  fulcrum  is  no  longer 
in  the  centre  of  gravity  ;  but  if  we  can  contrive  to 


72        ON  THE  MECHANICAL  POWERS. 

make  the  fulcrum  in  its  present  situation  become  the 
centre  of  gravity,  the  scales  will  again  balance  each 
other  ;  for  you  recollect  that  the  centre  of  gravity  is 
that  point  about  which  every  part  of  the  body  is  in 
equilibrium. 

Emily.  It  has  just  occurred  to  me  how  this  may 
be  accomplished  ;  put  a  great  weight  into  the  scale 
suspended  to  the  shortest  arm  of  the  lever,  and  a 
smaller  one  into  that  suspended  to  the  longest  arm. 
Yes,  1  have  discovered  it — look,  Mrs.  B.,  the  scale 
on  the  shortest  arm  will  carry  21bs.,  and  that  on  the 
longest  arm  only  one,  to  restore  the  balance,  (tig.  3.) 

Mrs.  B.  You  see,  therefore,  that  it  is  not  so  im- 
practicable as  you  imagined  to  make  a  heavy  body 
balance  a  light  one  ;  and  this  is  in  fact  the  means  by 
which  you  thought  an  imposition  in  the  weight  of 
goods  might.be  effected,  as  a  weight  often  or 
twelve  ounces  might  thus  be  made  to  balance  a  pound 
of  goods.  Let  us  now  take  off  the  scales,  that  we 
may  consider  the  lever  simply  ;  and  in  this  state  you 
see  that  the  fulcrum  is  no  longer  the  centre  of  gravi- 
ty ;  but  it  is,  and  must  ever  be,  the  centre  of  motion, 
as  it  is  the  only  point  which  remains  at  rest,  while 
the  other  parts  move  about  it. 

Caroline.  It  now  resembles  the  two  opposite  vanes 
of  a  windmill,  and  the  fulcrum  the  point  round  which 
they  move. 

Mrs.  B.  In  describing  the  motion  of  those  vanes, 
you  may  recollect  our  observing  that  the  farther  a 
body  is  from  the  axis  of  motion  the  greater  is  its 
velocity. 

Caroline.  That  I  remember  and  understood  per- 
fectly. 

Mrs.  B.  You  comprehend  then,  that  the  extremi- 
ty of  the  longest  arm  of  a  lever  must  move  with 
greater  velocity  than  that  of  the  shortest  arm  ? 

Emily.  No  doubt,  because  it  is  farthest  from  the 
centre  of  motion.  And  pray,  Mrs.  B.,  when  my 
brothers  play  at  see-saw,  is  not  the  plank  on  which 
they  ride  a  kind  of  lever  ? 


UN   THE  MECHANICAL  POWERS.  73 

Mrs,  B.  Certainly  ;  the  log  of  wood  which  sup- 
ports it  from  the  ground  is  the  fulcrum,  and  those  who 
ride  represent  the  power  and  the  resistance  at  each 
end  of  the  lever.  And  have  you  not  observed  that 
when  those  who  ride  are  of  equal  weight,  the  plank 
must  be  supported  in  the  middle  to  make  the  two 
arms  equal ;  whilst,  if  the  persons  diifer  in  weight, 
the  plank  must  be  drawn  a  little  further  over  the  prop, 
.>,  make  the  arms  unequal,  and  the  lightest  person, 
who  represents  the  resistance,  must  be  placed  at  the 
extremity  of  the  longest  arm. 

Caroline.  That  is  always  the  case  when  I  ride  on 
a  plank  with  my  youngest  brother;  1  have  observed  also 
that  the  lightest  person  has  the  best  ride,  as  he  moves 
both  further  and  quicker  ;  and  I  now  understand  that 
it  is  because  he  is  more  distant  from  the  centre  of 
motion. 

Mrs.  B.  The  greater  velocity  with  which  your 
little  brother  moves,  renders  his  momentum  equal  to 
yours. 

Caroline.  Yes  ;  I  have  the  most  gravity,  he  the 
greatest  velocity  ;  so  that  upon  the  whole  our  mo- 
mentums  are  equal. — But  you  said,  Mrs.  B.,  that  the 
power  should  be  greater  than  the  resistance  to  put 
the  machine  in  motion  ;  how  then  can  the  plank 
move  if  the  momentums  of  the  persons  who  ride  are 
equal. 

Mrs.  B.  Because  each  person  at  his  descent 
touches  the  ground  with  his  feet ;  the  reaction  of 
which  gives  him  an  impulse  which  increases  his  ve- 
locity ;  this  spring  is  requisite  to  destroy  the  equili- 
brium of  the  power  and  the  resistance,  otherwise, 
the  plank  would  not  move.  Did  you  ever  observe 
that  a  lever  describes  the  arc  of  a  circle  in  its  motion? 

Emily.  No  ;  it  appears  to  me  to  rise  and  descend 
perpendicularly  ;  at  least  I  always  thought  so. 

Mrs.  B.     I  believe  I  must  make  a  sketch  of  you 
and  your  brother  riding  on  a  plank,  in  order  to  con- 
vince you  of  your  error,  (fig.  4.  pi.  IV.)     You  may 
now  observe  that  a  lever  can  move  only  round  the 
7 


74        ON  THE  MECHANICAL  POWERS. 

fulcrum,  since  that  is  the  centre  of  motion  ;  it  would, 
be  impossible  for  you  to  rise  perpendicularly  to  the 
point  A,  or  for  your  brother  to  descend  in  a  straight 
line  to  the  point  B  ;  yon  must  in  rising  and  he  in  de- 
scending describe  arcs  of  your  respective  circles. 
This  drawing  shows  you  also  how  much  superior  his 
velocity  must  be  to  yours  ;  for  if  you  could  swing 
quite  round,  you  would  each  complete  your  respec- 
tive circles  in  the  same  time. 

Caroline.  My  brother's  circle  being  much  the 
largest,  he  must  undoubtedly  move  the  quickest. 

Mrs.  B.  Now  tell  me,  do  you  think  that  your 
brother  could  raise  you  as  easily  without  the  aid  of  a 
lever? 

Caroline.  Oh  no,  he  could  not  lift  me  off  the 
ground. 

Mrs.  B.  Then  1  think  you  require  no  further 
proof  of  the  power  of  a  lever,  since  you  see  what  it 
enables  your  brother  to  perform. 

Caroline,  I  now  understand  what  you  meant  by 
saying,  that  in  mechanics  motion  was  opposed  to  mat- 
ter, for  it  is  my  brother's  velocity  w|iich  overcomes 
my  weight. 

Mrs.  B.  You  may  easily  imagine  what  enormous 
weights  may  be  raised  by  levers  of  this  description, 
for  the  longer  the  acting  part  of  the  lever  in  compari- 
son to  the  resisting  part,  the  greater  is  the  effect  pro- 
duced by  it ;  because  the  greater  is  the  velocity  of 
the  power  compared  to  that  of  the  weight. 

There  are  three  different  kinds  of  levers;  in  the 
first  the  fulcrum  is  between  the  power  and  the  weight. 

Caroline.  This  kind  then  comprehends  the  seve- 
ral levers  you  have  described. 

Mrs.  B.  Yes,  when  in  levers  of  the  first  kind,  the 
fulcrum  is  equally  between  the  power  and  the  weight, 
as  in  the  balance  the  power  must  be  greater  than  the 
weight,  in  order  to  move  it ;  for  nothing  can  in  this 
case  be  gained  by  velocity  ;  the  two  arms  of  the  le- 
ver being  equal,  the  velocity  of  their  extremities 
must  be  so  likewise.     The  balance  is  therefore  of  no 


ON  THE  MECHANICAL  POWERS.        iO 

assistance  as  a  mechanical  power,  but  it  is  extremely 
tiseful  to  estimate  the  respective  weights  of  bodies. 

But  when  (fig.  6.)  the  fulcrum  F  of  a  lever  is  not 
equally  distant  from  the  power  and  the  weight,  and 
that  the  power  P  acts  at  the  extremity  of  the  longest 
arm,  it  may  be  less  than  the  weight  W,  its  deficiency 
being  compensated  by  its  superior  velocity ;  as  we 
observed  in  the  sce-saw. 

Emily.  Then  when  we  want  to  lift  a  great  weight, 
we  must  fasten  it  to  the  shortest  arm  of  a  lever,  and 
apply  our  strength  to  the  longest  arm  ? 

Mrs.  B.  If  the  case  will  admit  of  your  putting 
the  end  of  the  lever  under  the  weight,  no  fastening 
will  be  required ;  as  you  will  perceive  by  stirring  the 
fire. 

Emily.  Oh  yes!  the  poker  is  a  lever  of  the  first 
kind,  the  point  where  it  rests  against  the  bars  of  the 
grate,  whilst  I  am  stirring  the  fire,  is  the  fulcrum  ;  the 
short  arm,  or  resisting  part  of  the  lever,  is  employed 
in  lifting  the  weight,  which  is  the  coals,  and  my  hand 
is  the  power  applied  to  the  longest  arm,  or  acting  part 
of  the  lever. 

Mrs.  B.  Let  me  hear,  Caroline,  whether  you  can 
equally  well  explain  this  instrument,  which  is  compos- 
ed of  two  levers,  united  in  one  common  fulcrum. 

Caroline.     A  pair  of  scissars  ! 

Mrs.  B.  You  are  surprised,  but  if  you  examine 
their  construction,  you  will  discover  that  it  is  the 
power  of  the  lever  that  assists  us  in  cutting  with  scis- 
sars. 

Caroline.  Yes ;  I  now  perceive  that  the  point  at 
which  the  two  levers  are  screwed  together,  is  the 
fulcrum  ;  the  handles,  to  which  the  power  of  the  fin- 
gers is  applied,  are  the  extremities  of  the  acting  part 
of  the  levers,  and  the  cutting  part  of  the  scissars  are 
the  resisting  parts  of  the  levers  :  therefore,  the  long- 
er the  handles  and  the  shorter  the  points  of  the  scis- 
sars, the  more  easily  yon  cut  with  them. 

Emily.  That  I  have  often  observed,  for  when  I 
cut  paste-board  or  any  hard  substance,  I  always  make 


76  ox  THE  MECHANICAL  POWERS. 

use  of  that  part  of  the  scissars  nearest  the  screw  or 
rivet,  and  J  now  understand  why  it  increases  the  pow- 
er of  cutting;  hut  I  confess  that  I  never  should  have 
discovered  scissars  to  have  been  double  levers  ;  and 
pray  are  not  snuffers  levers  of  a  similar  description  ? 

Mrs.  B.  Yes,  and  most  kinds  of  pincers  ;  the 
great  power  of  which  consists  in  the  resisting  part  of 
the  lever  being  very  short  in  comparison  of  the  acting 
part. 

Caroline.  And  of  what  nature  are  the  two  other 
kinds  of  levers  ? 

Mrs.  B.  In  levers  of  the  second  kind,  the  weight, 
instead  of  being  at  one  end,  is  situated  between  the 
power  and  the  fulcrum,  (fig.  6.) 

Caroline.  The  weight  and  the  fulcrum  have  here 
changed  places  ;  and  what  advantage  is  gained  by  this 
kind  of  lever  ? 

Mrs.  B.  In  moving  it,  the  velocity  of  the  power 
must  necessarily  be  greater  than  that  of  the  weight, 
as  it  is  more  distant  from  the  centre  of  the  motion. 
Have  you  ever  seen  your  brother  move  a  snow-ball 
by  means  of  a  strong  stick,  when  it  became  too  heavy 
for  him  to  move  without  assistance  ? 

Caroline.  Oh  yes  ;  and  this  was  a  lever  of  the  se- 
cond order  ;  (fig.  7.)  the  end  of  the  stick,  which  he 
thrusts  under  the  ball,  and  which  rests  on  the  ground, 
becomes  the  fulcrum  ;  the  ball  is  the  weight  to  be 
moved,  and  the  power  his  hands  applied  to  the  other 
end  of  the  lever.  In  this  instance  there  is  an  immense 
difference  in  the  length  of  the  arms  of  the  lever  ;  for 
the  weight  is  almost  close  to  the  fulcrum. 

Mrs.  B.  And  the  advantage  gained  is  proportional 
to  this  difference.  Fishermen's  boats  are  by  levers 
of  this  description  raised  from  the  ground  to  be 
launched  into  the  sea,  by  means  of  slippery  pieces  of 
board  which  are  thrust  under  the  keel.  The  most 
common  example  that  we  have  of  levers  of  the  second 
kind  is  in  the  doors  of  our  apartments. 

Emily.     The  hinges  represent  the  fulcrum,  oiir 


ON  THE  MECHANICAL  POWERS.        77 

hands  the  power  applied  to  the  other  end  of  the  lever  ; 
but  where  is  the  weight  to  be  moved  ? 

Mrs.  B.  The  door  is  the  weight,  and  it  conse- 
quently occupies  the  whole  of  the  space  between  the 
power  and  the  fulcrum.  Nutcrackers  are  double  le- 
vers of  this  kind  :  the  hinge  is  the  fulcrum,  the  nut 
the  resistance,  and  the  hands  the  power. 

In  levers  of  the  third  kind  (fig.  8.),  the  fulcrum  is 
again  at  one  of  the  extremities,  the  weight  or  resist- 
ance at  the  other,  and  it  is  now  the  power  which  is 
applied  between  the  fulcrum  and  the  resistance. 

Emily.  The  fulcrum,  the  weight,  and  the  power, 
then,  each  in  their  turn,  occupy  some  part  of  the 
middle  of  the  lever  between  its  extremities.  But  in 
this  third  kind  of  lever,  the  weight  being  farther  from 
the  centre  of  motion  than  the  power,  the  difficulty  of 
raising  it  seems  increased  rather  than  diminished. 

Mrs.  B.  That  is  very  true  ;  a  lever  of  this  kind  is 
therefore  never  used,  unless  absolutely  necessary, 
as  is  the  case  in  lifting  up  a  ladder  perpendicularly  in 
order  to  place  it  against  a  wall ;  the  man  who  raises 
it  cannot  place  his  hands  on  the  upper  part  of  the 
ladder,  the  power,  therefore,  is  necessarily  placed 
much  nearer  the  fulcrum  than  the  weight. 

Caroline,  Yes,  the  hands  are  the  power,  the 
ground  the  fulcrum,  and  the  upper  part  of  the  ladder 
the  weight. 

Mrs.  B.  Nature  employs  this  kind  of  lever  in  the 
structure  of  the  human  frame.  In  lifting  a  weight 
with  the  hand,  the  lower  part  of  the  arm  becomes  a 
lever  of  the  third  kind  ;  the  elbow  is  the  fulcrum,  the 
muscles  of  the  fleshy  part  of  the  arm  the  power  ;  and 
as  these  are  nearer  to  the  elbow  than  the  hand,  it  is 
necessary  that  their  power  should  exceed  the  weight 
to  be  raised. 

Emily.  Is  it  not  surprising  that  nature  should  have 
furnished  us  with  such  disadvantageous  levers  ? 

Mrs.  B,  The  disadvantage,  in  respect  to  power, 
is  more  than  counterbalanced  by  the  convenience  re- 
sulting from  this  structure  of  the  arm  j  and  it  is  no 
7*. 


78        ON  THE  MECHANICAL  POWERS, 

doubt  that  which  is  best  adapted  to  enable  it  to  per- 
form its  various  functions. 

We  have  dwelt  so  long  on  the  lever,  that  we  must 
reserve  the  examination  of  the  other  mechanical  pow- 
ers to  our  next  interview. 


^^' 


Fich    2. 


PLATE    V. 


Awrv^x 


CONVERSATION  VL 


ON  THE  MECHANICAL  POWERS. 

Of  the  Pulley.^Of  the  Wheel  arid  Axle.— Of  the  In- 
clined Plane. — Of  the  Wedge. — Of  the  Screw. 

MRS.  B.  The  pulley  is  the  second  mechanical 
power  we  'are  to  examine.  You  both,  I  suppose, 
have  seen  a  pulley  ? 

Caroline.  Yes,  frequently  :  it  is  a  circular  and 
flat  piece  of  wood  or  metal,  with  a  string  which  runs 
in  a  groove  round  it ;  by  means  of  which  a  weight 
may  be  pulled  up  ;  thus  pulleys  are  used  for  drawing 
up  curtains. 

Mrs.  B.  Yes  ;  but  in  that  instance  the  pulleys 
are  fixed,  and  do  not  increase  the  power  to  raise  the 
weights,  as  you  will  perceive  by  this  figure,  (plate  V. 
fig  1.)  Observe  that  the  fixed  pulley  is  on  the  same 
principle  as  the  lever  of  a  pair  of  scales,  in  which 
the  fulcrum  F  being  in  the  centre  of  gravity,  the 
power  P  and  the  weight  W,  are  equally  distant  from 
it,  and  no  advantage  is  gained. 

Emily.  Certainly  ;  if  P  represents  the  power  em- 
ployed to  raise"  the  weight  W,  the  power  must  be 
greater  than  the  weight  in  order  to  move  it.  But  of 
what  use  then  are  pulleys  in  mechanics  ? 

Mrs.  B.  The  next  figure  represents  a  pulley 
which  is  not  fixed,  (fig.  2.)  and  thus  situated  you  will 
perceive  that  it  affords  us  mechanical  assistance.  In 
order  to  raise  the  weight  (W)  one  inch,  P,  the  pow- 


80        ON  THE  MECHANICAL  POWERS. 

er,  must  draw  the  strings  B  and  C  one  inch  each  ; 
the  whole  string  is  therefore  shortened  two  inches, 
while  the  weight  is  raised  only  one. 

Emily.  That  I  understand  :  if  P  drew  the  string 
but  one  inch,  the  weight  would  be  raised  only  half 
an  inch,  because  it  would  shorten  the  strings  B  and 
C  half  an  inch  each,  and  consequently  the  pulley, 
with  the  weight  attached  to  it,  can  be  raised  only 
half  an  inch. 

Caroline.  I  am  ashamed  of  my  stupidity  ;  but  I 
confess  that  I  do  not  understand  this ;  it  appears  to 
me  that  the  weight  would  be  raised  as  much  as  the 
string  is  shortened  by  the  power. 

Mrs.  B.  I  will  endeavour  to  explain  it  more 
clearly.  I  fasten  this  string  to  a  chair  and  draw  it 
towards  me  ;  I  have  now  shortened  the  string,  by 
the  act  of  drawing  it,  one  yard. 

Caroline.  And  the  chair,  as  I  supposed,  has  ad- 
vanced one  yard. 

Mrs.  B.  This  exemplifies  the  nature  of  a  single 
^xed  pulley  only.  Now  unfasten  the  string,  and  re- 
place the  chair  where  it  stood  before.  In  order  to 
represent  the  moveable  pulley,  we  must  draw  the 
chair  forwards  by  putting  the  string  round  it ;  one 
end  of  the  string  may  be  fastened  to  the  leg  of  the 
table,  and  I  shall  draw  the  chair  by  the  other  end  of 
the  string.  I  have  again  shortened  the  string  one 
yard  ;  how  much  has  the  chair  advanced  ? 

Caroline.  I  now  understand  it ;  the  chair  repre- 
sents the  weight  to  which  the  moveable  pulley  is  at- 
tached ;  and  it  is  very  clear  that  the  weight  can  be 
drawn  only  half  the  length  you  draw  the  string.  I 
believe  the  circumstance  that  perplexed  me  was,  that 
1  did  not  observe  the  difference  that  results  from  the 
weight  being  attached  to  the  pulley,  instead  of  being 
fastened  to  the  string,  as  is  the  case  in  the  fixed  pul- 
ley. 

Emily.  But  I  do  not  yet  understand  the  advantage 
of  pulleys  ;  they  seem  to  me  to  increase  rather  than 
diminish  the  difficulty  of  raising  weights,  since  you 


ON  THE  MECHANICAL  POWERS.        81 

must  draw  the  string  double  the  length  that  you 
raise  the  weighty  whilst  with  a  single  pulley,  or 
without  any  pulley,  the  weight  is  raised  as  much  as 
the  string  is  shortened. 

J^lrs.  B.  The  advantage  of  a  moveable  pulley 
consists  in  dividing  the  difficulty  ;  we  must  draw,  it 
is  true,  twice  the  length  of  the  string,  but  then  only 
half  the  strength  is  required  that  would  be  necessary 
to  raise  the  weight  without  the  assistance  of  a  move- 
able pulley. 

Emily.  So  that  the  difficulty  is  overcome  in  the 
same  manner  as  it  would  be,  by  dividing  the  weight 
into  two  equal  parts,  and  raising  them  successively. 

Mrs.  B.  Exactly.  You  must  observe,  that  with 
a  moveable  pulley  the  velocity  of  the  power  is  double 
that  of  the  weight,  since  the  power  P  (fig.  2.)  moves 
two  inches  whilst  the  weight  W  moves  one  inch  ; 
therefore  the  power  need  not  be  more  than  half  the 
weight  to  make  their  momentum^  equal. 

Caroline.  Pulleys  act  then  on  the  same  principle 
as  the  lever,  the  deficiency  of  strength  of  the  power 
being  compensated  by  its  superior  velocity. 

Mrs.  B.  You  will  find,  that  all  mechanical  power 
is  founded  on  the  same  principle. 

Emily.  But  may  it  not  be  objected  to  pulleys,  that 
a  longer  time  is  required  to  raise  a  weight  by  their 
aid  than  without  it ;  for  what  you  gain  in  power  you 
lose  in  time  ? 

Mrs.  B.  That,  my  dear,  is  the  fundamental  law 
in  mechanics  :  it  is  the  case  with  the  lever,  as  well 
as  the  pulley  ;  and  you  will  find  it  to  be  so  with  all 
the  other  mechanical  powers. 

Caroline.  I  do  not  see  any  advantage  in  the  me- 
chanical powers  then,  if  what  we  gain  by  them  one 
way  is  lost  another. 

Mrs.  B.  Since  we  are  not  able  to  increase  our 
natural  strength,  is  not  that  science  of  wonderful 
utility,  by  means  of  which  we  may  reduce  the  resist- 
ance or  weight  of  any  body  to  the  level  of  our 
strength  ?   This  the  mechanical  powers  enable  us  to 


82         ON  THE  MECHANICAL  POWERS. 

accomplish,  by  dividing  the  resistance  of  a  body  into 
parts  which  we  can  successively  overcome.  It  is 
true,  as  you  observe,  that  it  requires  a  sacrifice  of 
time  to  attain  this  end,  but  you  must  be  sensible  how 
very  advantageously  it  is  exchanged  for  power :  the 
utmost  exertion  we  can  make  adds  but  little  to  our 
natural  strength,  whilst  we  have  a  much  more  un- 
limited command  of  time.  You  can  now  understand, 
that  the  greater  the  number  of  pulleys  connected  by 
a  string  the  more  easily  the  weight  is  raised,  as  the 
difficulty  is  divided  amongst  the  number  of  strings, 
or  rather  of  parts  into  which  the  string  is  divided  by 
the  pulleys.  Several  pulleys  thus  connected,  form 
what  is  called  a  system,  or  tackle  of  pulleys,  (fig.  3.) 
You  may  have  seen  them  suspended  from  cranes  to 
raise  goods  into  warehouses,  and  in  ships  to  draw  up 
the  sails. 

Emily.  But  since  a  fixed  pulley  affords  us  no  me- 
chanical aid,  why  is  it  ever  used  ? 

Mrs.  B.  Though  it  does  not  increase  our  power, 
it  is  frequently  useful  for  altering  its  direction.  A 
single  pulley  enables  us  to  draw  up  a  curtain  by  draw- 
ing dozvn  the  string  connected  with  it ;  and  we  should 
be  much  at  u  loss  to  accomplish  this  simple  opera- 
tion without  its  assistance. 

Caroline.  There  would  certainly  be  some  diffi- 
culty in  ascending  to  the  head  of  the  curtain,  in  order 
to  draw  it  up.  Indeed,  I  now  recollect  having  seen 
workmen  raise  small  weights  by  this  means,  which 
seemed  to  answer  a  very  useful  purpose. 

Mrs.  B.  In  shipping,  both  the  advantages  of  an 
increase  of  power  and  a  change  of  direction,  by 
means  of  pulleys,  are  united  ;  for  the  sails  are  raised 
up  the  masts  by  the  sailors  on  deck,  from  the  change 
of  direction  which  the  pulley  effects,  and  the  labour 
is  facilitated  by  the  mechanical  power  of  a  corbbina- 
tion  of  pulleys. 

Emily.  But  the  pulleys  on  ship-board  do  not  ap- 
pear to  me  to  be  united  in  the  manner  you  have 
shown  us. 


ON  THE  MECHANICAL  POWERS.        83 

Mrs.  B.  They  are,  I  believe,  generally  connect- 
ed, as  described  in  figure  4,  both  for  nautical,  and  a 
variety  of  other  purposes  ;  but  in  whatever  manner 
pulleys  are  connected  by  a  single  string,  the  mecha- 
nical power  is  the  same. 

The  third  mechanical  power  is  the  wheel  and  axle. 
Let  us  suppose  (plate  VI.  fig.  5.)  tlie  weight  W  to 
be  a  bucket  of  water  in  a  well,  which  we  raise  by 
winding  the  rope,  to  which  it  is  attached,  round  the 
axle  ;  if  this  be  done  without  a  wheel  to  turn  the 
axle,  no  mechanical  assistance  is  received.  The 
axle  without  a  wheel  is  as  impotent  as  a  single  fixed 
pulley,  or  a  lever,  whose  fulcrum  is  in  the  centre  ;  but 
add  the  wheel  to  the  axle,  and  you  will  immediately 
find  the  bucket  is  raised  with  much  less  difficulty. 
The  velocity  of  the  circumference  of  the  wheel  is  as 
much  greater  than  that  of  the  axle,  as  it  is  further 
from  the  centre  of  motion  ;  for  the  wheel  describes 
a  great  circle  in  the  same  space  of  time  that  the  axle 
describes  a  small  one  ;  therefore  the  power  is  increas- 
ed in  the  same  proportion  as  the  circumference  of  the 
wheel  is  greater  than  that  of  the  axle.  If  the  velocity 
of  the  wheel  is  twelve  times  greater  than  that  of  the 
axle,  a  power  nearly  twelve  times  less  than  the  weight 
of  the  bucket  would  be  able  to  raise  it. 

Emily.  The  axle  acts  the  part  of  the  shorter  arm 
of  the  lever,  the  wheel  that  of  the  longer  arm. 

Caroline.  In  raising  water,  there  is  commonly,  I 
believe,  instead  of  a  wheel  attached  to  the  axle,  on- 
ly a  crooked  handle,  which  answers  the  purpose  of 
winding  the  rope  round  the  axle,  and  thus  raising 
the  bucket. 

Mrs.  B.  In  this  manner  (fig.  6.)  :  now  if  you  ob- 
serve the  dotted  circle  which  the  handle  describes 
in  winding  up  the  rope,  you  will  perceive  that  the 
branch  of  the  handle  A,  which  is  united  to  the  axle, 
represents  the  spoke  of  a  wheel,  and  answers  the 
purpose  of  an  entire  wheel ;  the  other  branch  B  af- 
fords no  mechanical  aid,  merely  serving  as  a  handle 
to  turn  the  wheel. 


^4  ON  TlTE  MECHANICJAL  POWERS. 

Wheels  are  a  very  essential  part  of  most  ma- 
chines :  they  are  employed  in  various  ways  ;  but, 
when  fixed  to  the  axle,  their  mechanical  power  is 
always  the  same  ;  that  is,  as  the  circumference  of 
the  wheel  exceeds  that  of  the  axle,  so  much  will  the 
energy  of  its  power  be  increased. 

Caroline.  Then  the  larger  the  wheel  the  greater 
must  be  its  effect. 

Mrs.  B.  Certainly.  If  you  have  ever  seen  any 
considerable  mills  or  manufactures,  you  must  have 
admired  the  immense  wheel,  the  revolution  of  which 
puts  the  whole  of  the  machinery  into  motion  ;  and 
though  so  great  an  effect  is  produced  by  it,  a  horse 
or  two  has  sufficient  power  to  turn  it  ;  sometimes  a 
stream  of  water  is  used  for  that  purpose,  but  of  late 
years,  a  steam-engine  has  been  found  both  the  most 
powerful  and  the  most  convenient  mode  of  turning 
the  wheel. 

Caroline.  Do  not  the  vanes  of  a  windmill  repre- 
sent a  wheel,  Mrs.  B. 

Mrs.  B.  Yes  ;  and  in  this  instance  we  have  the 
advantage  of  a  gratuitous  force,  the  wind,  to  turn  the 
wheel.  One  of  the  great  benefits  resulting  from  the 
use  of  machinery  is,  that  it  gives  us  a  sort  of  empire 
over  the  powers  of  nature,  and  enables  us  to  make 
them  perform  the  labour,  which  would  otherwise  fall 
to  the  lot  of  man.  When  a  current  of  wind,  a  stream 
of  water,  or  the  expansive  force  of  steam,  performs 
our  task,  we  have  only  to  superintend  and  regulate 
their  operations. 

The  fourth  mechanical  power  is  the  inclined 
plane  ;  this  is  nothing  more  than  a  slope,  or  declivi- 
ty, frequently  used  to  facilitate  the  drawing  up  of 
weights.  It  is  not  difficult  to  understand,  that  a 
weight  may  much  more  easily  be  drawn  up  a  slope 
than  it  can  be  raised  the  same  height  perpendicu- 
larly. But  in  this,  as  well  as  the  other  mechanical 
powers,  the  facility  is  purchased  by  a  loss  of  time 
(fig.  7  )  ;  for  the  weight,  instead  of  moving  directly 
from  A  to  C,  must  move  from  B  to  C,  and  as  the 


ON  THE  MECHANICAL  POWERb.        86 

length  of  the  plane  is  to  its  height,  so  much  is  the 
resistance  of  the  weight  diminished. 

Emily.  Yes  ;  for  the  resistance,  instead  of  being 
confined  to  the  short  line  A  C,  is  spread  over  the 
long  line  B  C. 

Mrs.  B.  The  wedge,  which  is  the  next  mechani- 
cal power,  is  composed  of  two  inclined  planes:  (fig. 
8.)  you  may  have  seen  wood-cutters  use  it  to  cleave 
wood.  The  resistance  consists  in  the  cohesive  at- 
traction of  the  wood,  or  any  other  body  which  the 
wedge  is  employed  to  separate  ;  and  the  advantage 
gained  by  this  power  is  in  the  proportion  of  half  its 
width  to  its  length  ;  for  while  the  wedge  forces  asun- 
der the  coherent  particles  of  the  wood  to  A  and  B,  it 
penetrates  downwards  as  iar  as  C. 

Emily.  The  wedge,  then,  is  rather  a  compound 
than  a  distinct  mechanical  power,  since  it  is  compos- 
ed of  two  inclined  planes. 

Mrs.  B.  It  is  so.  All  cutting  instruments  are  con- 
structed upon  the  principle  of  the  inclined  plane,  or 
the  wedge  :  those  that  have  but  one  edge  sloped,  Uke 
the  chisel,  may  be  referred  to  the  inclined  plane  : 
whilst  the  axe,  the  hatchet,  and  the  knife  (when  used 
to  split  asunder)  are  used  as  wedges. 

Caroline.  But  a  knife  cuts  best  when  it  is  drawu 
across  the  substance  it  is  to  divide.  We  use  it  thus 
in  cutting  meat,  we  do  not  chop  it  to  pieces. 

Mrs.  B.  The  reason  of  this  is,  that  the  edge  of  a 
knife  is  really  a  very  fine  saw,  and  therefore  acts  best 
when  used  Uke  that  instrument. 

The  screw,  which  is  the  last  mechanical  power,  is 
more  complicated  than  the  others.  You  will  see  by 
this  figure,  (fig.  9.)  that  it  is  composed  of  two  parts, 
the  screw  and  the  nut.  The  screw  S  is  a  cylinder, 
with  a  spiral  protuberance  coiled  round  it,  called 
the  thread  ;  the  nut  N  is  perforated  to  contain  the 
screw,  and  the  inside  of  the  nut  has  a  spiral  groove, 
made  to  fit  the  spiral  thread  of  the  screw. 

Caroline,     It  is  just  like  this  little  box,  the  lid  of 

8 


86  ON  THE  MECHANICAL  POWERS'. 

which  screws  on  the  box  as  you  have  described  ;  but 
what  is  this  handle  which  projects  from  the  nut  ? 

Mrs.  B.  It  is  a  lever,  which  is  attached  to  the 
nut,  without  which  the  screw  is  never  used  as  a  me- 
chanical power  ;  the  nut  with  a  lever  L  attached  to 
it,  is  commonly  called  a  winch.  The  power  of  the 
screw,  complicated  as  it  appears,  is  referable  to  one 
of  the  most  simple  of  the  mechanical  powers ; 
which  of  them  do  yon  think  it  is  ? 

Caroline.  In  appearance,  it  most  resembles  the 
wheel  and  axle. 

Mrs.  B.  The  lever,  it  is  true,  has  the  effect  of  a 
wheel,  as  it  is  the  means  by  which  you  wind  the  nut 
round  ;  but  the  lever  is  not  considered  as  composing 
a  part  of  the  screw,  though  it  is  true,  that  it  is  neces- 
sarily attached  to  it.  But  observe,  that  the  lever, 
considered  as  a  wheel,  is  not  fastened  to  the  axle  or 
screw,  but  moves  round  it,  and  in  so  doing,  the  nut 
either  rises  or  descends,  according  to  the  way  in 
which  you  turn  it. 

Emily.  The  spiral  thread  of  the  screw  resembles, 
I  think,  an  inclined  plane  :  it  is  a  sort  of  slope,  by 
means  of  wliich  the  nut  ascends  more  easily  than 
it  would  do  if  raised  perpendicularly  ;  and  it  serves  to 
support  it  when  at  rest. 

Mrs.  B.  Very  well  ;  if  you  cut  a  slip  of  paper  in 
the  form  of  an  inclined  plane,  and  wind  it  round  your 
pencil,  which  will  represent  the  cylinder,  you  will  find 
that  it  makes  a  spiral  line,  corresponding  to  the  spiral 
protuberance  of  the  screw.  (Fig.  10.) 

Emily.  Very  true  ;  the  nut  then  ascends  an  in- 
clined plane,  but  ascends  it  in  a  spiral,  instead  of  a 
straight  line  ;  the  closer  the  thread  of  the  screw,  the 
more  easy  the  ascent ;  it  is  like  having  shallow  in- 
stead of  steep  steps  to  ascend. 

Mrs.  B.  Yes  ;  excepting  that  the  nut  takes  no 
steps,  it  gradually  winds  up  or  down  ;  then  observe, 
that  the  closer  the  threads  of  the  screw,  the  greater 
the  number  of  revolutions  the  winch  must  make  :  so 


ON  THE  MECHANICAL  POWERS.         87 

that  we  return  to  the  old  principle — what  is  saved  in 
power  is  lost  in  time. 

Emily.  Cannot  the  power  of  the  screw  be  in- 
creased also,  by  lengthening  the  lever  attached  to  the 
nut  ? 

Mrs.  B.  Certainly.  The  screw  with  the  addition 
of  the  lever,  forms  a  very  powerful  machine,  employ- 
ed either  for  compression  or  to  raise  heavy  weights. 
It  is  used  by  book-binders,  to  press  the  leaves  of 
books  together  ;  it  is  used  also  in  cider  and  wine  pres- 
ses, in  coining,  and  for  a  variety  of  other  purposes. 

All  machines  are  composed  of  one  or  more  of 
these  six  mechanical  powers  we  have  examined  :  I 
have  but  one  more  remark  to  make  to  you,  relative  to 
them,  which  is,  that  friction  in  a  considerable  degree 
diminishes  their  force,  allowance  must  therefore  al- 
ways be  made  for  it  in  the  construction  of  machinc- 

Caroline.  By  friction  do  you  mean  one  part  of 
the  machine  rubbing  against  another  part  contiguous 
to  it? 

Mrs.  B.  Yes  ;  friction  is  the  resistance  which 
bodies  meet  with  in  rubbing  against  each  other  ; 
there  is  no  such  thing  as  perfect  smoothness  or  even- 
ness in  nature  :  polished  metals,  though  they  wear 
that  appearance  more  than  any  other  bodies,  are  far 
from  really  possessing  it ;  and  their  inequalities  may 
frequently  be  perceived  through  a  good  magnifying 
glass.  When,  therefore,  the  surfaces  of  the  two 
bodies  come  into  contact,  the  prominent  parts  of  the 
one  will  often  fall  into  the  hollow  parts  of  the  other, 
and  occasion  more  or  less  resistance  to  motion. 

Caroline.  But  if  a  machine  is  made  of  polished 
metal,  as  a  watch  for  instance,  the  friction  must  be 
very  trifling  ? 

Mrs.  B.  In  proportion  as  the  surfaces  of  bodies 
are  well  polished,  the  friction  is  doubtless  diminish- 
ed ;  but  it  is  always  considerable,  and  it  is  usually 
computed  to  destroy  one  third  of  the  power  of  a  ma- 
chine.     Oil  or  grease  is  used  to   lessen   friction  : 


o8         ON  THE  MECHANICAL  POWERS. 

it  acts  as  a  polish  by  filling  up  the  cavities  of  the  rub- 
bing surfaces,  and  thus  making  them  slide  more  easily 
over  each  other. 

Caroline.  Is  it  for  this  reason  that  wheels  are 
greased,  and  the  locks  and  hinges  of  doors  oiled  ? 

Mrs.  B.  Yes  ;  in  these  instances  the  contact  of 
the  rubbing  surfaces  is  so  close,  and  the  rubbing  so 
continual,  that  notwithstanding  their  being  polished 
and  oiled,  a  considerable  degree  of  friction  is  pro- 
duced. 

There  are  two  kinds  of  friction  ;  the  one  occasion- 
ed by  the  sliding  of  the  flat  surface  of  a  body,  the 
other  by  the  rolling  of  a  circular  body  :  the  friction 
resulting  from  the  first  is  much  the  most  considera- 
ble, for  great  force  is  required  to  enable  the  sliding 
body  to  overcome  the  resistance  which  the  asperities 
of  the  surfices  in  contact  oppose  to  its  motion,  and 
it  must  be  either  lifted  over,  or  break  through  them  ; 
whilst  in  the  other  kind  of  friction,  the  rough  parts 
roll  over  each  other  with  comparative  facility  ;  hence 
it  is,  that  wheels  are  often  used  for  the  sole  purpose 
of  diminisliing  the  resistance  of  friction. 

Emily.  This  is  one  of  the  advantages  of  carriage- 
wheels  ;  is  it  not  ? 

Mrs.  B.  Yes  ;  and  the  larger  the  circumference 
of  the  wheel  the  more  readily  it  can  overcome  any 
considerable  obstacles,  such  as  stones,  or  inequalities 
in  the  road.  When,  in  descending  a  steep  hill,  we 
fasten  one  of  the  wheels,  we  decrease  the  velocity 
of  the  carriage,  by  increasing  the  friction. 

Caroline.  That  is  to  say,  by  converting  the  roll- 
ing friction  into  the  dragging  friction.  And  when 
you  had  casters  put  to  the  legs  of  the  table,  in  order 
to  move  it  more  easily,  you  changed  the  dragging  in- 
to the  rolling  friction. 

Mrs.  B.  There  is  another  circumstance  which 
we  have  already  noticed,  as  diminishing  the  motiop 
of  bodies,  and  which  greatly  affects  the  power  of 
machines.  This  is  the  resistance  of  the  medium 
in  which  a  machine  is  worked.     All  fluids,  whether 


ON  THE  MECHANICAL  POWERS.  89 

of  the  nature  of  air  or  of  water,  are  called  me- 
diums ;  and  their  resistance  is  proportioned  to  their 
density  ;  for  the  more  matter  a  body  contains,  the 
greater  the  resistance  it  will  oppose  to  the  motion  of 
another  body  striking  against  it. 

Emily.  It  would  then  be  much  more  difficult  to 
work  a  machine  under  water  than  in  the  air  ? 

Mrs.  B.  Certainly,  if  a  machine  could  be  worked 
in  vacuo,  and  without  friction,  it  would  be  perfect  ; 
but  this  is  unattainable  ;  a  considerable  reduction  of 
power  must  therefore  be  allowed  for  the  resistance 
of  the  air. 

We  shall  here  conclude  our  observations  on  the 
mechanical  powers.  At  our  next  meeting  I  shall  en- 
deavour to  give  you  an  explanation  of  the  motion  of 
the  heavenly  bodies. 


S* 


CONVERSATION  VI. 


CAUSES  OF  THE  EARTH'S  ANNUAL 
MOTION. 

Of  the  Planets,  and  their  Motion — Of  the  Diurnal  Mo' 
Hon  of  the  Earth  and  Planets. 

CAROLINE.  I  am  come  to  you  to-day  quite 
elated  with  the  spirit  of  opposition,  Mrs.  B.  ;  for  I 
have  discovered  such  a  powerful  objection  to  your 
theory  of  attraction,  that  I  doubt  whether  even  your 
conjuror  Newton,  with  his  magic  wand  of  attraction, 
will  be  able  to  dispel  it. 

Mrs.  B.  Well,  my  dear,  pray  what  is  this  weighty 
objection  ? 

Caroline.  You  say  that  bodies  attract  in  propor- 
tion to  the  quantity  of  matter  they  contain,  now  we 
all  know  the  sun  to  be  much  larger  than  the  earth  : 
why,  therefore,  does  it  not  attract  the  earth  ;  you 
will  not,  I  suppose,  pretend  to  say  that  we  are  fall- 
ing towards  the  sun  ? 

Emily.  FJowever  plausible  your  objection  ap- 
pears, Caroline,  1  think  you  place  too  much  reliance 
upon  it :  when  any  one  has  given  such  convincing 
proofs  of  sagacity  and  wisdom  as  Sir  Isaac  Newton, 
when  we  find  that  his  opinions  are  universally  re- 
ceived and  adopted,  is  it  to  be  expected  that  any  ob- 
jection we  can  advance  should  overturn  them  ? 

Caroline.  Yet  I  confess  that  I  am  not  inclined  to 
yield   implicit  faith  even  to  opinions  of  the  great 


Fi^.l. 


FLATS  VI. 


CAUSES,    Arc.  91 

Newton  ;  for  what  purpose  are  we  endowed  with 
reason,  if  we  are  denied  the  privilege  of  making  use 
of  it,  by  judging  for  ourselves  ? 

Mrs.  B.  It  is  reason  itself  which  teaches  us,  that 
when  we,  novices  in  science,  start  objections  to  the- 
ories established  by  men  of  acknowledged  wisdom, 
we  should  be  diffident  rather  of  our  own  than  of 
their  opinion.  I  am  far  from  wishing  to  lay  the  least 
restraint  on  your  questions;  j^ou  cannot  be  better 
convinced  of  the  truth  of  a  system,  than  by  finding 
that  it  resists  all  your  attacks,  but  I  would  advise 
you  not  to  advance  your  objections  with  so  much  con- 
fidence, in  order  that  the  discovery  of  their  fallacy 
may  be  attended  with  less  mortification.  In  answer 
to  that  you  have  just  proposed,  I  can  only  say,  that 
the  earth  really  is  attracted  by  the  sun. 

Caroline.  Take  care  at  least  that  we  are  not  con- 
sumed by  him,  Mrs.  B. 

Mrs.  B.  We  are  in  no  danger  :  but  our  magician 
Newton,  as  you  are  pleased  to  call  him,  cannot 
extricate  himself  from  this  difficulty  without  the  aid 
of  some  cabilistical  figures,  which  I  must  draw  for 
liim. 

Let  us  suppose  the  earth,  at  its  creation,  to  have 
been  projected  forwards  into  universal  space  ;  we 
know  that  if  no  obstacle  impeded  its  course,  it  would 
proceed  in  the  same  direction,  and  with  a  uniform 
velocity  for  ever.  In  fig.  1.  plate  VI.,  A  represents 
the  earth,  and  S  the  sun.  We  shall  suppose  the 
earth  to  be  arrived  at  the  point  in  which  it  is  repre- 
sented in  the  figure,  having  a  velocity  which  would 
carry  it  on  to  B  in  the  space  of  one  month  ;  whilst 
the  sun's  attraction  would  bring  it  to  C  in  the  same 
space  of  time.  Observe  that  the  two  fi^rces  of  pro- 
jection and  attraction  do  not  act  in  opposition,  but 
perpendicularly,  or  at  a  right  angle  to  each  other. 
Can  you  tell  me  now,  how  the  earth  will  move  ? 

Emily.  I  recollect  your  teaching  us  that  a  body 
acted  upon  by  two  forces  perpendicular  to  each  other 
would  move  in  the  diagonal  of  a  parallelogram  ;  if, 


92  CAUSES  or  the 

therefore,  I  complete  the  parallelogram  by  drawing 
the  lines  CD,  B  D,  the  earth  will  move  in  the  dia- 
gonal A  D. 

Mrs.  B.  A  ball  struck  by  two  forces  acting  per- 
pendiciilarl}"^  to  each  other,  it  is  true,  moves  in  the 
diagonal  of  a  parallelogram  ;  but  you  must  observe 
that  the  force  of  attraction  is  continually  acting  upon 
our  terrestrial  ball,  and  producing  an  incessant  devi- 
ation from  its  course  in  a  right  line,  which  converts 
it  into  that  of  a  curved  line  ;  every  point  of  which 
may  be  considered  as  constituting  the  diagonal  of  an 
infinitely  small  parallelogram. 

Let  us  detain  the  earth  a  moment  at  the  point  D, 
and  consider  how  it  will  be  affected  by  the  combined 
action  of  the  two  forces  in  its  new  situation.  It  still 
retains  its  tendency  to  fly  off  in  a  straight  line  ;  but 
a  straight  line  would  now  carry  it  away  to  F,  whilst 
the  sun  would  attract  it  in  the  direction  D  S  ;  how 
then  will  it  proceed  ? 

Emily.  It  will  go  on  in  a  curve  line  in  a  direction 
between  that  of  the  two  forces. 

Mrs.  B.  In  order  to  know  exactly  what  course  the 
earth  will  follow,  draw  another  parallelogram  similar 
to  the  first,  in  which  the  line  D  F  describes  the  force 
of  projection,  and  the  line  D  S,  that  of  attraction  ; 
and  you  will  find  that  the  earth  will  proceed  in  the 
curve  line  D  G. 

Caroline.  You  must  now  allow  me  to  draw  a  pa- 
rallelogram, Mrs.  B.  Let  me  consider  in  what  direc- 
tion will  the  force  of  projection  now  impel  the  earth. 

Mrs.  B.  First  draw  a  line  from  the  earth  to  the 
sun,  representing  the  force  of  attraction  ;  then  de- 
scribe the  force  of  projection  at  a  right  angle  to  it. 

Caroline.  The  earth  will  then  move  in  the  curve 
G  I,  of  the  parallelogram  G  li  1  K. 

Mrs.  B.  You  recollect  that  a  body  acted  upon  by 
two  forces,  moves  through  a  diagonal  in  the  same 
time  that  it  would  have  moved  through  one  of  the 
sides  of  the  parallelogram,  were  it  acted  upon  by  one 
force  only.     The  earth  has  passed  through  the  diago- 


earth's  annual  motion.  93 

nals  of  these  three  parallelograms  in  the  space  of 
three  months,  and  has  performed  one  quarter  of  a 
circle  ;  and  on  the  same  principle  it  will  go  on  till  it 
has  completed  the  whole  of  the  circle.  It  will  then 
recommence  a  course,  which  it  has  pursued  ever 
since  it  first  issued  from  the  hand  of  its  Creator,  and 
which  there  is  every  reason  to  suppose  it  will  conti- 
nue to  follow,  as  long  as  it  remains  in  existence. 

Emily.  What  a  grand  and  beautiful  effect,  result- 
ing from  so  simple  a  cause  ! 

Caroline.  It  affords  an  example,  on  a  magnificent 
«cale,  of  the  circular  motion  which  you  tau2;ht  us  in 
mechanics.  The  attraction  of  the  sun  is  the  centri- 
petal force,  which  confines  the  earth  to  a  centre  ; 
and  the  impulse  of  projection  the  centrifugal  force, 
which  impels  the  earth  to  quit  the  sun  and  fly  off  in  a 
tangent. 

Mrs.  B.  Exactly  so.  A  simple  mode  of  illustra- 
ting the  effect  of  these  combined  forces  on  the  earth, 
is  to  cut  a  slip  of  card  in  the  form  of  a  right  angle, 
(fig.  2.  plate  VI.)  to  describe  a  small  circle  at  the  an- 
gular point  representing  the  earth,  and  to  fasten  the 
extremity  of  one  of  the  legs  of  the  angle  to  a  fixed 
point,  which  we  shall  consider  as  the  sun.  Thus  si- 
tuated, the  angle  will  represent  both  the  centrifugal 
and  centripetal  forces  ;  and  if  you  draw  it  round  the 
fixed  point,  you  will  see  how  the  direction  of  the  cen- 
trifugal force  varies,  constantly  forming  a  tangent  to 
the  circle  in  which  the  earth  moves,  as  it  is  constant- 
ly at  a  right  angle  with  the  centripetal  force. 

Emily.  The  earth,  then,  gravitates  towards  the 
sun  without  the  slightest  danger  either  of  approach- 
ing nearer  or  receding  further  from  it.  How  admi- 
rably this  is  contrived!  If  the  two  forces  which  pro- 
duce this  circular  motion  had  not  been  so  accurately 
adjusted,  one  would  ultimately  have  prevailed  over 
the  other,  and  we  should  either  have  approached  so 
near  the  sun  as  to  have  been  burnt,  or  have  receded 
so  far  from  it  as  to  have  been  frozen. 

Mrs.  B.     What  will  you  say,  my  dear,  when  I  tell 


94  CAUSES    OF    THE 

you,  that  these  two  forces  are  not,  in  fact,  so  pro- 
portioned as  to  produce  circular  motion  in  the  earth? 

Caroline.  You  must  explain  to  us,  at  least,  in  what 
manner  we  avoid  the  threatened  destruction. 

Mrs.  B.  Let  us  suppose  that  when  the  earth  is  at 
A,  (fig.  3.)  its  projectile  force  should  not  have  given 
it  a  velocity  sufficient  to  counterbalance  that  of  gra- 
vity, so  as  to  enable  these  powers  conjointly  to  carry 
it  round  the  sun  in  a  circle  ;  the  earth,  instead  of  de- 
scribing the  line  A  C,  as  in  the  former  figure,  vvill 
approach  nearer  the  sun  in  the  line  A  B. 

Caroline.  Under  these  circumstances,  I  see  not 
what  is  to  prevent  our  approaching  nearer  and  nearer 
the  sun  till  we  fall  into  it ;  for  its  attraction  increases 
as  we  advance  towards  it,  and  produces  an  accelerated 
velocity  in  the  earth,  which  increases  the  danger. 

Mrs.  B.  And  there  is  yet  another  danger,  of 
which  you  are  not  aware.  Observe,  that  as  the 
earth  approaches  the  sun,  the  direction  of  its  projec- 
tile force  is  no  longer  perpendicular  to  that  of  attrac- 
tion, but  inclines  more  nearly  to  it.  When  the  earth 
reaches  that  part  of  its  orbit  at  B,  the  force  of  projec- 
tion would  carry  it  to  D,  which  brings  it  nearer  the 
sun  instead  of  bearing  it  away  from  it. 

Emily.  If,  then,  we  are  driven  by  one  power  and 
drawn  by  the  other  to  this  centre  of  destruction,  how 
is  it  possible  for  us  to  escape  ? 

Mrs.  B.  A  little  patience,  and  you  will  find  that 
we  are  not  without  resource.  The  earth  continues 
approaching  the  sun  with  a  uniformly  increasing  ac- 
celerated motion,  till  it  reaches  the  point  E ;  in  what 
direction  will  the  projectile  force  now  impel  it? 

Emily.  In  the  direction  E  F.  Here  then  the  two 
forces  act  perpendicularly  to  each  other,  and  the 
earth  is  situated  just  as  it  was  in  the  preceding  figure  ; 
therefore,  from  this  point,  it  should  revolve  round  the 
sun  in  a  circle. 

Mrs.  B.  No,  all  the  circumstances  do  not  agree. 
In  motion  round  a  centre,  you  recollect  that  the  cen- 
trifugal force  increases  with  the  velocity  of  the  body. 


earth's  annual  motion.  95 

or,  in  other  words,  the  quicker  it  moves  the  stronger 
is  its  tendency  to  fly  ofl'  in  a  right  line.  When  the 
earth,  therefore,  arrives  at  E,  its  accelerated  motion 
will  have  so  far  increased  its  velocity,  and  consequent- 
ly its  .centrifugal  force,  that  the  latter  will  prevail  over 
the  force  of  attraction,  and  drag  the  earth  away  from 
the  sun  till  it  reaches  G. 

Caroline.  It  is  thus,  then,  that  we  escape  from 
the  dangerous  vicinity  of  the  sun  ;  and  in  proportion 
as  we  recede  from  it,  the  force  of  its  attraction,  and, 
consequently,  the  velocity  of  the  earth's  motion,  are 
diminished. 

Mrs.  B.  Yes.  From  G  the  direction  of  projection 
is  towards  H,  that  of  attraction  towards  S,  and  the 
earth  proceeds  between  them  with  a  uniformly  re- 
tarded motion,  till  it  has  completed  its  revolution. 
Thus  you  see,  that  the  earth  travels  round  the  sun, 
not  in  a  circle,  but  an  ellipsis,  of  which  the  sun 
occupies  one  of  the  foci;  and  that  in  its  course  the 
earth  alternately  approaches  and  recedes  from  it, 
without  any  danger  of  being  either  swallowed  up,  or 
of  being  entirely  carried  away  from  it. 

Caroline.  And  1  observe,  that  what  I  apprehended 
to  be  a  dangerous  irregularity,  is  the  means  by  which 
the  most  perfect  order  and  harmony  are  produced ! 

Emily.  The  earth  travels,  then,  at  a  very  unequal 
rate,  its  velocity  being  accelerated  as  it  approaches 
the  sun,  and  retarded  as  it  recedes  from  it. 

Mrs.  B.  It  is  mathematically  demonstrable,  that, 
in  moving  round  a  point  towards  which  it  is  attracted, 
a  body  passes  over  equal  areas  in  equal  times.  The 
whole  of  the  space  contained  within  the  earth's  orbit, 
is,  in  fig.  4,  divided  into  a  number  of  areas,  or  spaces, 
1,  2,  3,  4,  &.C.  all  of  which  are  of  equal  dimensions, 
though  of  very  different  forms  ;  some  of  them,  you 
see,  are  long  and  narrow,  others  broad  and  short ;  but 
they  each  of  them  contain  an  equal  quantity  of  space. 
An  imaginary  line  drawn  from  the  centre  of  the  earth 
to  that  of  the  sun,  and  keeping  pace  with  the  earth 
in  its  revolution,  passes  over  equal  areas  in  equal 


96  CAUSES    OF    THE 

times ;  that  is  to  say,  if  it  is  a  month  going  from  A  to 
B,  it  will  be  a  month  going  from  B  to  C,  and  another 
from  C  to  E,  and  so  on. 

Caroline.  What  long  journeys  the  earth  has  to 
perform  in  the  course  of  a  month,  in  one  part  of  her 
orbit,  and  how  short  they  are  in  the  other  part! 

Mrs.  B.  The  inequality  is  not  so  considerable  as 
appears  in  this  figure ;  for  the  earth's  orbit  is  not  so 
eccentric  as  it  is  there  described ;  and,  in  reality, 
differs  but  little  from  a  circle  :  that  part  of  the  earth's 
orbit  nearest  the  sun  is  called  its  perihelion,  that  part 
most  distant  from  the  sun  its  aphelion;  and  the  earth 
is  above  three  millions  of  miles  nearer  the  sun  at  its 
perihelion  than  at  its  aphelion. 

Emily.  I  think  I  can  trace  a  consequence  from 
these  different  situations  of  the  earth  ;  is  it  not  the 
cause  of  summer  and  winter? 

Mrs.  B.  On  the  contrary ;  during  the  height  of 
summer,  the  earth  is  in  that  part  of  its  orbit  which  is 
most  distant  from  the  sun,  and  it  is  during  the  severity 
of  winter  that  it  approaches  nearest  to  it. 

Emily.  That  is  very  extraordinary;  and  how  then 
do  you  account  for  the  heat  being  greatest  when  we 
are  most  distant  from  the  sun  ? 

Mrs.  B.  The  difference  of  the  earth's  distance 
from  the  sun  in  summer  and  winter,  when  compared 
with  its  total  distance  from  the  sun,  is  but  inconsidera- 
ble. The  earth,  it  is  true,  is  above  three  millions  of 
miles  nearer  the  sun  in  winter  than  in  summer ;  but 
that  distance,  however  great  it  at  first  appears,  sinks 
into  insignificance  in  comparison  of  95  millions  of 
miles,  which  is  our  mean  distance  from  the  sun.  The 
change  of  temperature,  arising  from  this  difference, 
would  scarcely  be  sensible  ;  were  it  not  completely 
overpowered  by  other  causes  which  produce  the  va- 
riations of  the  seasons ;  but  these  I  shall  defer  explain- 
ing, till  we  have  made  some  further  observations  on 
the  heavenly  bodies. 

Caroline.  And  should  not  the  sun  appear  smaller 
in  summer,  when  it  is  so  much  further  from  us  ? 


earth's  annual  motion.  97 

Mrs.  B.  It  actually  does,  when  accurately  mea- 
sured ;  but  the  apparent  difference  in  size  is,  I  be- 
lieve, not  perceptible  to  the  naked  eye. 

Emily.  Then,  since  the  earth  moves  with  greatest 
velocity  in  that  part  of  its  orbit  nearest  the  sun,  it 
must  have  completed  its  journey  through  one  half  of 
its  orbit  in  a  shorter  time  than  the  other  half? 

Mrs.  B.  Yes,  it  is  about  seven  days  longer  per- 
forming the  summer  half  of  its  orbit  than  the  winter 
half. 

The  revolution  of  all  the  planets  round  the  sun  is 
the  result  of  the  same  causes,  and  is  performed  in 
the  same  manner  as  that  of  the  earth. 

Caroline.     Pray  what  are  the  planets  ? 

Mrs.  B.     They  are  those  celestial  bodies,  which 
-revolve  like  our  earth  about  the  sun  ;  they  are  sup- 
posed to   resemble  the  earth  also  in  many  other  re- 
spects ;  and  we  are  led  by  analogy  to  suppose  them 
to  be  inhabited  worlds. 

Caroline.  I  have  heard  so  ;  but  do  you  not  think 
such  an  opinion  too  great  u  stretch  of  the  imagina- 
tion ? 

Mrs.  B.  Some  of  the  planets  are  proved  to  be 
larger  than  the  earth  ;  it  is  only  their  immense  dis- 
tance from  us,  which  renders  their  apparent  dimen- 
sions so  small.  Now,  if  we  consider  them  as  enor- 
mous globes,  instead  of  small  twinkling  spots,  we 
shall  be  led  to  suppose,  that  the  Almighty  would  not 
have  created  them  merely  for  the  purpose  of  giving 
us  a  little  light  in  the  night,  as  it  was  formerly  ima- 
gined, and  we  should  find  it  more  consistent  with 
our  ideas  of  the  Divine  wisdom  and  beneficence,  to 
suppose  that  these  celestial  bodies  should  be  created 
for  the  habitation  of  beings,  who  are,  like  us,  bless- 
ed by  His  providence.  Both  in  a  moral  as  well  as 
a  physical  point  of  view,  it  appears  to  me  more  ra- 
tional to  consider  the  planets  as  worlds  revolving 
round  the  sun  ;  and  the  fixed  stars  as  other  suns, 
each  of  them  attended  by  their  respective  system  of 
planets,  to  which  they  impart  theif  influence  ?  We 
9 


98  CAUSES    OF    THE 

have  brought  our  telescopes  to  such  a  degree  of  per- 
fection, that  from  the  appearances  which  the  moon 
exhibits  when  seen  through  them,  we  have  very  good 
reason  to  conclude,  that  it  is  a  habitable  globe,  for 
though  it  is  true,  that  we  cannot  discern  its  towns 
and  people,  we  can  plainly  perceive  its  mountains 
and  valleys  ;  and  some  astronomers  have  gone  so  far 
as  to  imagine  they  discovered  volcanos. 

Emily.  If  the  fixed  stars  are  suns,  with  planets 
revolving  round  them,  why  should  we  not  see  those 
planets  as  well  as  their  suns  ? 

Mrs.  B.  In  the  first  place,  we  conclude  that  the 
planets  of  other  systems,  (like  those  of  our  own,)  are 
much  smaller  than  the  suns  which  give  them  light  ; 
therefore  at  so  great  a  distance  as  to  make  the  suns 
appear  like  fixed  stars,  the  planets  would  be  quite 
invisible.  Secondly,  the  light  of  the  planets  being 
only  reflected  light,  is  much  more  feeble  than  that  of 
the  fixed  stars.  There  is  exactly  the  same  difference 
as  between  the  light  of  the  sun  and  that  of  the  moon; 
the  first  being  a  fixed  star,  the  second  a  planet. 

Emily.  But  if  the  planets  are  worlds  like  our 
earth,  they  are  dark  bodies  ;  and  instead  of  shining 
by  night,  we  should  see  them  only  by  daylight. — 
And  why  do  we  not  see  the  fixed  stars  also  by  day- 

light?" 

Mrs.  B.  Both  for  the  same  reason  ; — their  light 
is  so  faint,  compared  to  that  of  our  sun  reflected  by 
the  atmosphere,  that  it  is  entirely  eff'aced  by  it  :  the 
light  emitted  by  the  fixed  stars  may  probably  be  as 
strong  as  that  of  our  sun,  at  an  equal  distance  ;  but 
being  so  much  more  remote,  it  is  difl'used  over  a 
greater  space,  and  is  consequently  proportionally 
■weakened. 

Caroline.  True  ;  I  can  see  much  better  by  the 
light  of  a  candle  that  is  near  me,  than  by  that  of  one 
at  a  great  distance.  But  I  do  not  understand  what 
makes  the  planets  shine  ? 

Mrs.  B.  What  is  it  that  makes  the  steel  buttons 
on  your  brother's  coat  shine  ? 


earth's  annual   M0TI0I7.  99 

Caroline.  The  sun.  But  if  it  was  the  sun  which 
made  the  planets  shine,  we  should  see  them  in  the 
day-time,  when  the  sun  shone  upon  them  ;  or  if  the 
fjiintness  of  their  light  prevented  our  seeing  them  in 
the  day,  we  should  not  see  them  at  all,  for  the  sun 
cannot  shine  upon  them  in  the  night. 

Mrs.  B.  There  you  are  in  error.  But  in  order  to 
explain  this  to  you,  I  must  first  make  you  acquainted 
with  the  various  motions  of  the  planets. 

You  know,  that  according  to  the  laws  of  attraction, 
the  planets  belonging  to  our  system  all  gravitate  to- 
wards the  sun  :  and  that  this  force  combined  with 
that  of  projection,  will  occasion  their  revolution 
round  the  sun,  in  orbits  more  or  less  elliptical,  ac- 
cording to  the  proportion  which  these  two  forces 
bear  to  each  other. 

But  the  planets  have  also  another  motion  :  they 
revolve  upon  their  axes.  The  axis  of  a  planet  is  an 
imaginary  line  which  passes  through  its  centre,  and 
on  which  it  turns  ;  and  it  is  this  motion  which  pro- 
duces day  and  night.  With  that  side  of  the  planet 
facing  the  sun,  it  is  day  ;  and  with  the  opposite  side, 
which  remains  in  darkness,  it  is  night.  Our  earth, 
which  we  consider  as  a  planet,  is  24  hours  in  per- 
forming one  revolution  on  its  axis  :  in  that  period  of 
time,  therefore,  we  have  a  day  and  a  niglit ;  hence 
this  revolution  is  called  the  earth's  diurnal  or  daily 
motion  ;  and  it  is  this  revolution  of  the  earth  from 
west  to  east  which  produces  an  apparent  motion  of 
the  sun,  moon  and  stars  in  a  contrary  direction. 

Let  us  now  suppose  ourselves  to  be  beings,  inde- 
pendent of  any  planet,  travelling  in  the  skies,  and 
looking  upon  the  earth  in  the  same  point  of  view  as 
upon  the  other  planets. 

Caroline.  It  is  not  flattering  to  us,  its  inhabitants, 
to  see  it  make  so  insignificant  an  appearance. 

Mrs.  B.  To  those  who  are  accustomed  to  contem- 
plate it  in  this  light,  it  never  appears  more  glorious. 
We  are  taught  by  science  to  distrust  appearances  ; 
and  instead  of  considering  the  planets  as  little  stars, 


100  CAUSES    OF    THE 

we  look  np6n  them  either  as  hrilliant  suns  or  habitable 
worlds,  and  we  consider  the  whole  together  as  form- 
ing one  vast  and  magnificent  system,  worthy  of  the 
Divine  hand  b}'  which  it  was  created. 

Emily.  I  can  scarcely  conceive  the  idea  of  this 
immensity  of  creation  ;Mt  seems  too  sublime  for  our 
imagination  : — and  to  think  that  the  goodness  of  Pro- 
vidence extends  over  millions  of  worlds  throughout  a 
boundless  universe — Ah !  Mrs.  B.,  it  is  we  only  who 
become  trifling  and  insignificant  beings  in  so  magni- 
iScent  a  creation ! 

Mrs.  B.  This  idea  should  teach  us  humility,  but 
without  producing  despondency.  The  same  Almighty 
})and  which  guides  these  countless  worlds  in  their  un- 
deviating  course,  conducts  with  equal  perfection  the 
])lood  as  it  circulates  through  the  veins  of  a  fly,  and 
opens  the  eye  of  the  insect  to  behold  His  wonders. 
Notwithstanding  this  immense  scale  of  creation, 
therefore,  we  need  not  fear  to  be  disregarded  or  for- 
gotten. 

But  to  return  to  our  station  in  the  skies.  We 
were,  if  you  recollect,  viewing  the  earth  at  a  great 
distance,  in  appearance  a  little  star,  one  side  illumin- 
ed by  the  sun,  the  other  in  obscurity.  But  would  you 
believe  it,  Caroline,  many  of  the  inhabitants  of  this  little 
star  imagine  that  when  that  part  which  they  inhabit 
is  turned  from  the  sun,  darkness  prevails  throughout 
the  universe,  merely  because  it  is  night  with  them  ; 
whilst,  in  reality,  the  sun  never  ceases  to  shine  upon 
every  planet.  When,  therefore,  these  little  igno- 
rant beings  look  around  them  during  their  night, 
and  behold  all  the  stars  shining,  they  cannot  ima- 
gine why  the  planets,  which  are  dark  bodies,  should 
shine,  concluding,  that  since  the  sun  docs  not  illu- 
mine themselves,  the  whole  universe  must  be  in 
darkness. 

Caroline,  I  confess  that  I  was  one  of  these  igno- 
rant people  ;  but  I  am  now  very  sensible  of  the  ab- 
surdity of  such  an  idea.  To  the  inhabitants  of  the  other 
planets,  then,  we  must  appear  as  a  little  star  ? 


earth's  annual  motion.       101 

Mrs.  B.  Yes,  to  those  which  rerolve  round  our 
sun  ;  for  since  those  which  may  belong  to  other 
systems,  (and  whose  existence  is  only  hypothetical,) 
are  invisible  to  us,  it  is  probable,  that  we  also  are 
invisible  to  them. 

Emily.  But  they  may  see  our  sun  as  we  do  theirs, 
ip  appearance  a  fixed  star  ? 

Mrs.  B.  No  doubt  ;  if  the  beings  who  inhabit 
those  planets  are  endowed  with  senses  similar  to  ours. 
By  the  same  rule,  we  must  appear  as  a  moon  to  the 
inhabitants  of  our  moon  ;  but  on  a  larger  scale,  as 
the  surface  of  the  earth  is  about  thirteen  times  as 
large  as  that  of  the  moon. 

Emily.  The  moon,  Mrs.  B.,  appears  to  move  in 
a  different  direction,  and  in  a  different  manner  from 
the  stars  ? 

Mrs.  B.  I  shall  defer  the  explanation  of  the  mo- 
tion of  the  moon,  till  our  next  interview,  as  it  would 
prolong  our  present  lesson  too  much. 


9* 


CONVERSATION  VIL 


ON  THE  PLANETS. 

Of  the  Satellites  or  Moons. — Gravity  diminishes  as  the 
Square  of  the  Distance. —  Of  the  Solar  System. —  Of 
Comets — Constellations,  Signs  of  the  Zodiac. — Of 
Copernicus,  Newton,  4'C. 

MRS.  B.  The  planets  are  distinguished  into  pri- 
mary and  secondary.  Those  which  revolve  immedi- 
ately about  the  sun  are  called  primary.  Many  of  these 
are  attended  in  their  course  by  smaller  planets,  which 
revolve  around  them :  these  are  called  secondary 
planets,  satellites,  or  moons.  Such  is  our  moon, 
which  accompanies  the  earth,  and  is  carried  with  it 
round  the  sun. 

Emily.  How  then  can  you  reconcile  the  motion 
of  the  secondary  planets  to  the  laws  of  gravitation  ; 
for  the  sun  is  much  larger  than  any  of  the  primary 
planets  ;  and  is  not  the  power  of  gravity  proportion- 
al to  the  quantity  of  matter  ? 

Caroline.  Perhaps  the  sun,  though  much  larger, 
may  be  less  dense  than  the  planets.  Fire  you  know 
is  very  light,  and  it  may  contain  but  little  matter, 
though  of  great  magnitude. 

Mrs.  B.  We  do  not  knOw  of  what  kind  of  matter 
the  sun  is  made  ;  but  we  may  be  certain,  that  since 
it  is  the  general  centre  of  attraction  of  our  system  of 
planets,  it  must  be  the  body  which  contains  the  great- 
est quantity  of  matter  in  that  system. 

Yoa  must  recollect,  that  the  force  of  attraction  i* 


ON  THE  PLANETS.  10^ 

not  only  proportional  to  the  quantity  of  matter,  but  to 
the  degree  of  proximity  of  the  attractive  body  :  this 
power  is  weakened  by  being  diflfused,  and  diminishes 
as  the  squares  of  the  distances  increase.  The  square 
is  the  product  of  a  number  multiplied  by  itself;  so 
that  a  planet  situated  at  twice  the  distance  at  which 
we  are  from  the  sun  would  gravitate  four  times  less 
than  we  do  ;  for  the  product  of  two  multiplied  by  it- 
self is  four. 

Caroline.  Then  the  more  distant  planets  move 
slower  in  their  orbits  ;  for  their  projectile  force  must 
be  proportioned  to  that  of  attraction  ?  But  I  do  not 
see  how  this  accounts  for  the  motion  of  the  secondary 
round  the  primary  planets,  in  preference  to  the  sun  ? 

Emily.  Is  it  not  because  the  vicinity  of  the  pri- 
mary planets  renders  their  attraction  stronger  than 
that  of  the  sun  ? 

Mrs.  B.  Exactly  so.  But  since  the  attraction  be- 
tween bodies  is  mutual,  the  primary  planets  are  also 
attracted  by  the  satellites,  which  revolve  round  them. 
The  moon  attracts  the  earth,  as  well  as  the  earth  the 
moon  ;  but  as  the  latter  is  the  smaller  body,  her  at- 
traction is  proportionally  less  ;  therefore  neither  the 
earth  revolves  round  the  moon,  nor  the  moon  round 
the  earth  ;  but  they  both  revolve  round  a  point, 
which  is  their  common  centre  of  gravity,  and  which 
is  as  much  nearer  the  earth  than  the  moon,  as  the  gra- 
vity of  the  former  exceeds  that  of  the  latter. 

Emily.  Yes,  I  recollect  your  saying,  that  if  two 
bodies  were  fastened  together  by  a  wire  or  bar,  their 
common  centre  of  gravity  would  be  in  the  middle  of 
the  bar,  provided  the  bodies  were  of  equal  weight ; 
and  if  they  differed  in  weight,  it  would  be  nearer  the 
larger  body.  If  then  the  earth  and  moon  had  no  pro- 
jectile force  which  prevented  their  mutual  attraction 
from  bringing  them  together,  they  would  meet  at  their 
common  centre  of  gravity. 

Caroline.  The  earth  then  has  a  great  variety  of 
motions  :  it  revolves  round  the  sun,  upon  its  axis,  and 
round  the  point  towards  which  the  moon  attracts  it. 


104  ON  THE  PLANETS. 

Mrs.  B.  Just  so;  and  this  is  the  case  with  every 
planet  which  is  attended  by  satelhtes.  The  compli- 
cated effect  of  this  variety  of  motions,  produces  cer- 
tain irregularities,  which,  however,  it  is  not  necessa- 
ry to  notice  at  present. 

The  planets  act  on  the  sun  in  the  same  manner  as 
they  are  themselves  acted  on  by  their  satellites  ;  for 
attraction,  you  must  remember,  is  always  mutual ;  but 
the  gravity  0/  the  planets  (even  when  taken  collec- 
tively) is  so  trifling  compared  with  that  of  the  sun, 
that  they  do  not  cause  the  latter  to  move  so  much  as 
one  half  of  his  diameter.  The  planets  do  not,  there- 
fore, revolve  round  the  centre  of  the  sun,  but  round 
a  point  at  a  small  distance  from  its  centre,  about 
which  the  sun  also  revolves. 

Emily.     I  thought  the  sun  had  no  motion? 

Mrs.  B.  You  were  mistaken  ;  for,  besides  that 
which  I  have  just  mentioned,  which  is  indeed  very 
inconsiderable,  he  revolves  on  his  axis  ;  this  motion 
is  ascertained  by  observing  certain  spots  which  disap- 
pear, and  re-appear  regularly  at  stated  times. 

Caroline.  A  planet  has  frequently  been  pointed 
out  to  me  in  the  heavens  ;  but  I  could  not  perceive 
that  its  motion  differed  from  that  of  the  fixed  stars, 
which  only  appear  to  move. 

Mrs.  B.  The  great  distance  of  the  planets  renders 
their  motion  apparently  so  slow,  that  the  eye  is  not 
sensible  of  their  progress  in  their  orbit,  unless  we 
watch  them  for  some  considerable  length  of  time  :  in 
different  seasons  they  appear  in  different  parts  of  the 
heavens.  The  most  accurate  idea  1  can  give  you  of 
the  situation  and  motion  of  the  planets,  will  be  by  the 
examination  of  this  diagram,  (Plate  VII.  fig.  1.)  repre- 
senting the  solar  system,  in  which  you  will  find  every 
planet  with  its  orbit  delineated. 

Emily.  But  the  orbits  here  are  all  circular,  and 
you  said  that  they  were  elliptical.  The  planets  ap- 
pear, too,  to  be  moving  round  the  centre  of  the  sun  ; 
whilst  you  told  us,  that  they  moved  round  a  point  at 
a  little  distance  from  thence. 


PLATE   Vn. 


Fi^. 


Ft^.    2. 


Mars         yemis       Forth 

^'-y  "o     o     o 


Moon 


Hertchel 


n 


t)N  THE  PLACETS.  105 


Mrs.  B.  The  orbits  of  the  planets  nre  so  nearly 
circular,  and  the  common  centre  of  gravity  of  the  so- 
lar system  so  near  the  centre  of  the  sun,  that  these 
deviations  are  scarcely  worth  observing.  The  di- 
mensions of  the  planets,  in  their  true  proportions, 
you  will  find  delineated  in  fig.  2. 

Mercury  is  the  planet  nearest  the  sun ;  his  orbit  is 
consequently  contained  within  ours  ;  but  his  vicinity 
to  the  sun,  occasions  his  being  nearly  lost  in  the  bril- 
liancy of  his  rays  ;  and  when  we  see  the  sun,  he  is  so 
dazzling,  that  very  accurate  observations  cannot  be 
made  upon  Mercury.  He  performs  his  revolution 
round  the  sun  in  about  87  days,  which  is  consequent- 
ly the  length  of  his  year.  The  time  of  his  ro- 
tation on  his  axis  is  not  known  ;  his  distance  from  the 
sun  is  computed  to  be  37  millions  of  miles,  and  his 
diameter  3180  miles.  The  heat  of  this  planet  is  so 
great,  that  water  cannot  exist  there,  but  in  a  state  of 
vapour,  and  metals  would  be  liquified. 

Caroli7ie.     Oh,  what  a  dreadful  climate! 

Mrs.  B.  Though  we  could  not  live  there,  it  may 
be  perfectly  adapted  to  other  beings  destined  to  inha- 
bit it. 

Venus,  the  next  in  the  order  of  planets,  is  68  mil- 
lions of  miles  from  the  sun  :  she  revolves  about  her 
axis  in  23  hours  and  21  minutes,  and  goes  round  the 
sun  in  244  days  17  hours.  The  orbit  of  Venus  is  also 
within  ours  ;  during  one  half  of  her  course  in  it,  we 
see  her  before  sunrise,  and  she  is  called  the  morning 
star  ;  in  the  other  part  of  her  orbit,  she  rises  later 
than  the  sun. 

Caroline.  In  that  case,  we  cannot  see  her,  for  she 
must  rise  in  the  day  time  ? 

Mrs.  B.  True  ;  but  when  she  rises  later  than  the 
sun,  she  also  sets  later  ;  so  that  we  perceive  her  ap- 
proaching the  horizon  after  sunset :  she  is  then  call- 
ed Hesperus,  or  the  evening  star.  Do  you  recollect 
those  beautiful  lines  of  Milton  : 

Now  came  still  evening  on,  and  twilight  grav 
Had  in  her  sober  livery  all  things  clad;. 


f 


106  ON  THE  PLANETS. 

Silence  accompanied  ;  for  beast  and  bird, 
They  to  their  grassy  couch,  these  to  their  nests 
Were  slunk,  all  but  the  wakeful  nightingale  ; 
She  all  night  long  her  amorous  descant  sung; 
Silence  was  pleas'd  :  now  glowed  the  firmament 
With  living  saphirs:  Hesperus,  that  led 
The  starry  host,  rode  brightest,  till  the  m6on 
Rising  in  clouded  majesty,  at  length 
Apparent  queen  unveil'd  her  peerless  light, 
And  o'er  the  dark  her  silver  mantle  threw. 

The  planet  next  to  Venus  is  the  Earth,  of  which 
we  shall  soon  speak  at  full  length.  At  present  I  shall 
only  observe  that  we  are  95  millions  of  miles  distant 
from  the  sun,  that  we  perform  our  annual  revolution 
in  365  days  5  hours  and  49  minutes  ;  and  are  attend- 
ed in  our  course  by  a  single  moon. 

Next  follows  Mars.  He  can  never  come  between 
us  and  the  sun,  like  I\rercury  and  Venus  ;  his  motion 
is,  however,  very  perceptible,  as  he  may  be  traced 
to  different  situations  in  the  heavens  ;  his  distance 
from  the  sun  is  144  millions  of  miles  ;  he  turns 
rounds  his  axis  in  24  hours  and  39  minutes  ;  and  he 
performs  his  annual  revolution,  in  about  687  of  our 
days  :  his  diameter  is  4120  miles..  Then  follow  four 
very  small  planets,  Juno,  Ceres,  Pallas,  and  Vesta, 
which  have  been  recently  discovered,  but  whose  di- 
mensions and  distances  from  the  sun  have  not  been 
very  accurately  ascertained. 

Jupiter  is  next  in  order  :  this  is  the  largest  of  all 
the  planets.  He  is  about  490  millions  of  miles  from 
the  sun,  and  completes  his  annual  period  in  nearly 
twelve  of  our  years.  He  turns  round  his  axis  in 
about  ten  hours.  He  is  above  1200  times  as  big  as 
our  earth  ;  his  diameter  being  86,000  miles.  The 
respective  proportions  of  the  planets  cannot,  there- 
fore, you  see,  be  conveniently  delineated  in  a  dia- 
gram.    He  is  attended  by  four  moons. 

The  next  planet  is  Saturn,  whose  distance  from  the 
sun  is  about  900  millions  of  miles  ;  his  diurnal  rota- 
tion is  performed  in  10  hours  and  a  quarter  : — his  an- 
nual revolution  in  nearly  30  of  our  years.     His  dia- 


ON  THE  PLANETS.  107 

meter  is  79,000  miles.  This  planet  is  surrounded 
hy  a  luminous  ring,  the  nature  of  which,  astronomers 
are  much  at  a  loss  to  conjecture  ;  he  has  seven 
moons.  Lastly,  we  observe  the  Georgium  Sidus,  disco- 
vered by  Dr.  Herschel,  and  which  is  attended  by  six 
moons. 

Caroline.  How  charming;  it  must  be  in  the  distant 
planets,  to  see  several  moons  shining  at  the  eame 
time  ;  I  think  I  should  like  to  be  an  inhabitant  of  Ju- 
piter or  Saturn. 

Mrs.  B.  Not  long,  I  believe.  Consider  what  ex- 
treme cold  must  prevail  in  a  planet,  situated  as  Saturn 
is,  at  nearly  ten  times  the  distance  at  which  we  are  from 
the  sun.  Then  his  numerous  moons  are  far  from 
making  so  splendid  an  appearance  as  ours  ;  for  they 
can  reflect  only  the  light  which  they  receive  from  the 
sun  ;  and  both  light  and  heat  decrease  in  the  same 
ratio  or  proportion  to  the  distances  as  gravity.  Caa 
you  tell  me  now  how  much  more  light  we  enjoy 
than  Saturn  ? 

Caroline.  The  square  of  ten  is  a  hundred  ;  there- 
fore, Saturn  has  a  hundred  times  less — or  to  answer 
your  question  exactly,  we  have  a  hundred  times 
more  light  and  heat  than  Saturn — this  certainly  does 
not  increase  my  wish  to  become  one  of  tbe  poor 
wretches  who  inhabit  that  planet. 

Mrs.  B.  May  not  the  inhabitants  of  Mercury, 
with  equal  plausibility,  pity  us,  for  the  insupportable 
coldness  of  our  situation  ;  and  those  of  Jupiter  and 
Saturn  for  our  intolerable  heat  ?  The  x'Mmighty  Pow- 
er which  created  these  planets,  and  placed  them  in 
their  several  orbits,  has  no  doubt  peopled  them  with 
beings  whose  bodies  are  adapted  to  the  various  tem- 
peratures and  elements  in  which  they  are  situated. 
If  we  judge  from  the  analogy  of  our  own  earth,  or 
from  that  of  the  great  and  universal  beneficence  of 
Providence,  we  must  conclude  this  to  be  the  case. 

Caroline.  Are  not  comets  also  supposed  to  be 
planets  ? 

Mrs.  B.     Yes,   they  are  ;  for  by  the  re-appear- 


108  ON  THE  PLANETS. 

ance  of  some  of  them,  at  stated  times,  they  are 
known  to  revolve  round  the  sun,  but  in  orbits  so  ex- 
tremely eccentric,  that  they  disappear  for  a  great 
number  of  years.  If  they  are  inhabited,  it  must  be 
by  a  species  of  beings  very  different,  not  only  from 
the  inhabitants  of  this,  but  from  those  of  any  of  the 
other  planets,  as  they  must  experience  the  greatest 
vicissitudes  of  heat  and  cold  ;  one  part  of  their  orbit 
being  so  near  the  sun,  that  their  heat,  when  there, 
is  computed  to  be  greater  than  that  of  red-hot  iron  ; 
in  this  part  of  its  orbit,  the  comet  emits  a  luminous 
vapour,  called  the  tail,  which  it  gradually  loses  as  it 
recedes  from  the  sun  ;  and  the  comet  itself  totally 
disappears  from  our  sight,  in  the  more  distant  parts 
of  its  orbit,  which  extends  considerably  beyond  that 
of  the  furthest  planet. 

The  number  of  comets  belonging  to  our  system 
cannot  be  ascertained,  as  some  of  them  are  whole 
centuries  before  they  make  their  re-appearance. 
The  number  that  are  known  by  their  regular  re-ap- 
pearance is  only  three. 

Emily.     Pray,  Mrs.  B.,  what  are  the  constellations? 

Mrs.  B.  They  are  the  fixed  stars,  which  the  an- 
cients, in  order  to  recognise  them,  formed  into 
groups,  and  gave  the  names  of  the  figures  which  you 
find  delineated  on  the  celestial  globe.  In  order  to 
show  their  proper  situations  in  the  heavens,  they 
should  be  painted  on  the  internal  surface  of  a  hollow 
sphere,  from  the  centre  of  which  you  should  view 
them  ;  you  would  then  behold  them,  as  they  appear 
to  be  situated  in  the  heavens.  The  twelve  constel- 
lations, called  the  signs  of  the  zodiac,  are  those  which 
are  so  situated,  that  the  earth  in  its  annual  revolution 
passes  directly  between  them  and  the  sun.  Their 
names  are  Aries,  Taurus,  Gemini,  Cancer,  Leo,  Vir- 
go, Libra,  Scorpio,  Sagittarius,  Capricornus,  Aquari- 
us, Pisces  ;  the  whole  occupj'ing  a  complete  circle, 
or  broad  belt,  in  the  heavens,  called  the  zodiac. 
(Plate  VIIl.  fig.  1.)  Hence  a  right  line  drawn  from 
the  earth,  and  passing  through  the  sun,  would  reach 


TLATE  vm. 


ON  THE  PLANETS.  109 

one  of  these  constellations,  and  the  sun  is  said  to  be 
in  that  constellation  at  which  the  line  terminates:  thus, 
when  the  earth  is  at  A,  the  sun  would  appear  to  be 
in  the  constellation  or  sign  Aries  ;  when  the  earth  is 
at  B,  the  sun  would  appear  in  Cancer  ;  when  the 
earth  was  at  C,  the  sun  would  be  in  Libra  ;  and  when 
the  earth  was  at  D,  the  sun  would  be  in  Capricorn. 
This  circle,  in  which  the  sun  thus  appears  to  move, 
and  which  passes  through  the  middle  of  the  zodiac, 
is  called  the  ecliptic. 

Caroline.  But  many  of  the  stars  in  these  constel- 
lations appear  beyond  the  zodiac. 

Mrs.  B.  We  have  no  means  of  ascertaining  the 
distance  of  the  fixed  stars.  When,  therefore,  they 
are  said  to  be  in  the  zodiac,  it  is  merely  implied,  that 
they  are  situated  in  that  direction,  and  that  they  shine 
upon  us  through  that  portion  of  the  heavens  which 
we  call  the  zodiac. 

Emily.  But  are  not  those  large  bright  stars,  which 
are  called  stars  of  the  first  magnitude,  nearei*  to  us 
than  those  small  ones  which  we  can  scarcely  discern? 

Mrs.  B.  It  may  be  so  ;  or  the  difference  of  hze 
and  brilliancy  of  the  stars  may  proceed  from  their 
difference  of  dimensions  ;  this  is  a  point  which  as- 
tronomers are  not  enabled  to  determine.  Consider- 
ing them  as  suns,  I  see  no  reason  why  different  suns 
should  not  vary  in  dimensions,  as  well  as  the  planets 
belonging  to  them. 

Emily.  What  a  wonderful  and  beautiful  system  this  is, 
and  how  astonishing  to  think  that  every  fixed  star  ma/ 
probably  be  attended  by  a  similar  train  of  planets  I 

Caroline.  You  will  accuse  me  of  being  very  in- 
credulous, but  I  cannot  help  still  entertaining  some 
doubts,  and  fearing  that  there  is  more  beauty  than 
truth  in  this  system.  It  certainly  may  be  so  ;  but 
there  does  not  appear  to  me  to  be  sufficient  evidence 
to  prove  it.  It  seems  so  plain  and  obvious  that  the 
earth  is  motionless,  and  that  the  sun  and  stars  revolve 
round  it ; — your  solar  system,  you  must  allow,  is  di- 
rectly in  opposition  to  the  evidence  of  our  senses. 
10 


110  ON    THE    PLANETS. 

Mrs.  J5.  Our  senses  so  often  mislead  us,  that  we 
should  not  place  implicit  reliance  upon  them. 

Caroline.  On  what  then  can  we  rely,  for  do  we 
not  receive  all  our  ideas  through  the  medium  of  our 
senses  ? 

Mrs.  B.  It  is  true,  that  they  are  our  primary 
source  of  knowledge  ;  but  the  mind  has  the  power 
of  reflecting,  judging,  and  deciding  upon  the  ideas 
received  by  the  organs  of  sense.  This  faculty,  which 
we  call  reason,  has  frequently  proved  to  us,  that  our 
senses  are  liable  to  err.  If  you  have  ever  sailed  on 
the  water,  with  a  very  steady  breeze,  you  must  have 
seen  the  houses,  trees  and  every  object  move  while 
you  were  sailing. 

Caroline.  I  remember  thinking  so,  when  I  was 
very  young :  but  I  now  know  that  their  motion  is 
only  apparent.  It  is  true  that  my  reason,  in  this  case, 
corrects  the  error  of  my  sight. 

Mrs.  B.  It  teaclies  you,  that  the  apparent  motion 
of  the  objects  on  shore,  proceeds  from  your  being 
yourself  moving,  and  that  you  are  not  sensible  of 
yqpr  own  motion,  because  you  meet  with  no  resist- 
ance. It  is  only  when  some  obstacle  impedes  our 
motion,  that  we  are  conscious  of  moving;  and  if  you 
were  to  close  your  eyes  when  you  were  sailing  on 
calm  water,  with  a  steady  wind,  you  woujd  not  per- 
ceive that  you  moved,  for  you  could  not  feel  it,  and 
you  could  see  it  only  by  observing  the  change  of 
place  of  the  objects  on  shore.  So  it  is  with  the  mo- 
tion of  the  earth  ;  every  thing  on  its  surface,  and  the 
air  that  surrounds  it,  accompanies  it  in  its  revolution  ; 
it  meets  with  no  resistance  ;  therefore,  like  the  crew 
of  a  vessel  sailing  with  a  fair  wind,  in  a  calm  sea,  we 
arc  insensible  of  our  motion. 

Caroline.  But  the  principal  reason  why  the  crew 
of  a  vessel  in  a  calm  sea  do  not  perceive  the  motion, 
is,  because  they  move  exceedingly  slowly  ;  while  the 
earth,  you  say,  revolves  with  great  velocit3^ 

Mrs^  B.  It  is  not  because  they  move  slowly,  but 
because   they  move  steadily,   and   meet  with  no  ir- 


ON    THE    I'LAXETS.  HI 

regular  resistances,  that  the  crew  of  a  vessel  do  no! 
perceive  their  motion  ;  for  they  would  be  equally 
insensible  to  it,  with  the  strongest  wind,  provided  it 
were  steady,  that  they  sailed  with  it,  and  that  it  did 
not  agitate  the  water  ;  but  this  last  condition,  you 
know,  is  not  possible,  for  the  wind  will  always  pro- 
duce waves,  which  offer  more  or  less  resistance  to 
the  vessel,  and  then  the  motion  becomes  sensible 
because  it  is  unequal. 

Caroline.  But,  granting  this,  the  crew  of  a  vessel 
have  a  proof  of  their  motion,  though  insensible, 
which  the  inhabitants  of  the  earth  cannot  have — the 
apparent  motion  of  the  objects  on  shore. 

Mrs.  B.  Have  we  not  a  similar  proof  of  the  earth's 
motion,  in  the  apparent  motion  of  the  sun  and  stars. 
Imagine  the  earth  to  be  sailing  round  its  axis,  and 
successively  passing  by  every  star,  which,  like  the 
objects  on  land,  we  suppose  to  be  moving  instead 
of  ourselves.  1  have  heard  it  observed  by  an  aerial 
traveller  in  a  balloon,  that  the  earth  appears,  to  sink 
beneath  the  balloon,  instead  of  the  balloon  rising 
above  the  earth. 

It  is  a  law  which  we  discover  throughout  nature,  and 
worthy  of  its  great  Author,  that  all  its  purposes  are 
accomplished  by  the  most  simple  means  ;  and  what 
reason  have  we  to  suppose  this  law  infringed,  in  or- 
der that  we  may  remain  at  rest,  while  the  sun  and 
stars  move  round  us  ;  their  regular  motions,  which 
are  explained  by  the  laws  of  attraction  on  the  first 
supposition,  would  be  unintelligible  on  the  last,  and 
the  order  and  harmony  of  the  universe  be  destroyed. 
Think  what  an  immense  circuit  the  sun  and  stars 
would  make  daily,  were  their  apparent  motions  real. 
We  know  many  of  them  to  be  bodies  more  consider- 
able than  our  earth  ;  for  our  eyes  vainly  endeavour 
to  persuade  us,  that  they  are  little  brilliants  spark- 
ling in  the  heavens,  while  science  teaches  us  that 
they  are  immense  spheres,  whose  apparent  dimen- 
sions are  diminished  by  distance.  Why  then  should 
these  enormous  globes  daily  traverse -such  a  prodi- 


112  ON    THE    PLANETS. 

gions  space,  merely  to  prevent  the  necessity  of  our 
earth's  revolving  on  its  axis  ? 

Caroline.  I  think  I  must  now  be  convinced.  But 
3'ou  vpill,  I  hope,  allow  me  a  little  time  to  familiarize 
m^'^self  to  an  idea  so  diirerent  from  that  which  1  have 
been  accustomed  to  entertain.  And  pray,  at  what 
rate  do  we  move  ? 

Mrs.  B.  The  motion  produced  by  the  revolution 
of  the  earth  on  its  axis,  is  about  eleven  miles  a  mi- 
nute, to  an  inhabitant  of  London. 

Emily.  But  docs  not  every  part  of  the  earth  move 
with  the  same  velocity  ? 

Mrs.  B.  A  moment's  reflection  would  convince 
you  of  the  contrary  ;  a  person  at  the  equator  must 
move  quicker  than  one  situated  near  the  poles,  since 
they  both  perform  a  revolution  in  24  hours. 

Emily.  True,  the  equator  is  farthest  from  the  axis 
of  motion.  But  in  the  earth's  revolution  round  the 
sun,  every  part  must  move  with  equal  velocity  ? 

Mrs.  B.     Yes,  about  a  thousand  miles  a  minute. 

Caroline.  How  astonishing! — and  that  it  should 
be  possible  for  us  to  be  insensible  of  such  a  rapid  mo- 
tion. You  would  not  tell  me  this  sooner,  Mrs.  B.,  for 
fear  of  increasing  my  incredulity. 

Before  the  time  of  Newton,  was  not  the  earth  sup- 
posed to  be  in  the  centre  of  the  system,  and  the  sun, 
moon,  and  stars  to  revolve  round  it  ? 

Mrs.  B.  This  was  the  system  of  Ptolemy  in  an- 
cient times  ;  but  as  long  ago  as  the  beginning  of  the 
sixteenth  century  it  was  discarded,  and  the  solar  sys- 
tem, such  as  I  have  shown  you,  was  established  by 
the  celebrated  astronomer  Copernicus,  and  is  hence 
called  the  Copernican  system.  But  the  theory  of 
gravitation,  the  source  from  which  this  beautiful  and 
harmonious  arrangement  flows,  we  owe  to  the  pow- 
erful genius  of  Newton,  who  lived  at  a  much  later 
period. 

Emily.  It  appears,  indeed,  fiir  less  diflicult  to  trace 
by  observation  the  motion  of  the  planets,  than  to  di- 
vine by  what  power  they  are  impelled  and  guided.     I 


ON  THE  PLANETS.  113 

wonder  how  the  idea  of  gravitation  could  first  have 
occurred  to  Sir  Isaac  Newton  ? 

Mrs.  B.  It  is  said  to  have  been  occasioned  by  a 
circumstance  from  which  one  should  little  have  ex- 
pected so  grand  a  theory  to  have  arisen.  During 
the  prevalence  of  the  plague  in  the  year  1665,  New- 
ton retired  into  the  country  to  avoid  the  contagion  : 
when  sitting  one  day  in  his  orchard,  he  observed 
an  apple  fall  from  a  tree,  and  was  led  to  consider 
what  could  be  the  cause  which  brought  it  to  the 
ground. 

Caroline.  If  I  dared  to  confess  it,  Mrs.  B.,  I  should 
say  that  such  an  inquiry  indicated  rather  a  deficiency 
than  a  superiority  of  intellect.  I  do  not  understand 
how  any  one  can  wonder  at  what  is  so  natural  and  so 
common. 

Mrs.  B.  It  is  the  mark  of  superior  genius  to  find 
matter  for  wonder,  observation,  and  research,  in  cir- 
cumstances which,  to  the  ordinary  mind,  appear  tri- 
vial, because  they  are  common,  and  with  which  they 
are  satisfied,  because  they  are  natural,  without  re- 
flecting that  nature  is  our  grand  field  of  observation, 
that  within  it  is  contained  our  whole  store  of  know- 
ledge ;  in  a  word,  that  to  study  the  works  of  nature, 
is  to  learn  to  appreciate  and  admire  the  wisdom  of 
God.  Thus,  it  was  the  simple  circumstance  of  the 
fall  of  an  apple,  which  led  to  the  discovery  of  the 
laws  upon  whigh  the  Copernican  system  is  founded  ; 
and  whatever  credit  this  system  had  obtained  before, 
it  now  rests  upon  a  basis  from  which,  it  cannot  be 
shaken. 

Emily.  This  was  a  most  fortunate  apple,  and  more 
worthy  to  be  commemorated  than  all  those  that  have 
been  sung  by  the  poets.  The  apple  of  discord  for 
which  the  goddesses  contended  ;  the  golden  apples  by 
which  Atalanta  won  the  race;  nay,  even  the  applQ 
which  William  Tell  shot  from  the  head  of  his  son 
cannot  be  compared  to  this  ! 

10* 


CONVERSATION  Vllf. 


ON  THE  EARTH. 

Of  the  Terrestrial  Globe.— Of  the  Figure  of  the  Earth, 
— Of  the  Pendulum. — Of  the  Variation  of  the  Sea- 
sons, and  of  the  Length  of  Days  and  JVights. — Of 
the  causes  of  the  Heat  of  Summer. — Of  Solar,  Side- 
rial,  and  Equal  or  Mean  Time, 

MRS.  B.  As  the  earth  is  the  planet  in  wliich  we 
are  the  most  particuhirly  interested,  it  is  my  intention. 
this  mornina;,  to  explain  to  you  the  effects  resulting 
li'om  its  annual  and  diurnal  njotions  ;  but  for  this  pur- 
pose it  will  bo  necessary  to  make  you  acquainted  with 
the  terrestrial  globe  :  you  have  not  either  of  you,  I 
conclude,  learnt  the  use  of  the  g;h:)bes  ? 

Carnline.  No  ;  I  once  indeed  loarnt  by  heart  the 
names  of  the  lines  marked  on  the  globe,  but  as  1  was 
informed  they  were  only  imaginary  divisions,  they 
did  not  appear  to  me  worthy  of  much  attention,  and 
were  soon  fori^otten. 

Mrs.  B.  You  supposed,  then,  that  astronomers 
had  been  at  the  trouble  of  inventing  a  number  uf  lines 
to  little  purpose.  It  will  be  impossible  for  me  to  ex- 
plain to  you  the  particular  effects  of  the  earth's  mo- 
tion, without  your  having  acquired  a  knowledge  of 
these  lines  :  in  Plate  Vlll.  fig.  2.  you  will  find  them 
ail  delineated  :  and  you  mu'^t  learn  them  perfectly  if 
you  wish  to  make  any  proficiency  in  astronomy. 

Caroline.  I  was  taught  them  at  so  early  an  age 
that  I  could  not  understand  their  meaning  ;  and  I 
have  often  heard  you  say  that  the  only  use  of  words 
was  to  convey  ideas. 


ON  THE  EARTH.  lib 

Mrs.  B.  The  names  of  these  lines  would  have 
conveyed  ideas  of  the  tigures  they  were  designed  to 
express,  though  the  use  of  these  tigures  might  at  that 
time  have  been  too  difficult  for  you  to  understand. 
Childhood  is  the  season  when  impression*^  on  the  me- 
mory are  most  strongly  and  most  easily  made  :  it  is 
the  period  at  which  a  large  stock  of  ideas  should  be 
treasured  up,  the  application  of  which  we  may  learn 
when  the  understanding  is  more  developed.  It  is,  I 
think,  a  very  mistaken  notion  that  children  should  be 
taught  such  things  only  as  they  can  perfectly  under- 
stand. Had  you  been  early  made  acquainted  with  the 
terms  which  relate  to  figure  and  motion,  how  much  it 
would  have  facilitated  your  progress  in  natural  philo- 
sophy. I  have  been  obliged  to  confine  myself  to  the 
most  common  and  familiar  expressions,  in  explaining 
the  laws  of  nature,  though  I  am  convinced  that  ap- 
propriate and  scientific  terms  would  have  conveyed 
more  precise  and  accurate  ideas  ;  but  1  was  afraid  of 
not  being  understood. 

Emily.  You  may  depend  upon  our  learning  the 
names  of  these  lines  thoroughly,  Mrs.  B. ;  but,  before 
we  commit  them  to  memory,  will  you  have  the  good- 
ness to  explain  them  to  us  ? 

Mrs.  B.  Most  willingly.  This  globe,  or  sphere, 
represents  the  earth  ;  the  line  which  passes  through 
its  centre,  and  on  which  it  turns,  is  called  its  axis  : 
and  the  two  extremities  of  the  axis,  A  and  B,  are  the 
poles,  distinguished  by  the  names  of  the  north  and  the 
south  pole.  The  circle  C  D,  which  divides  the  globe 
into  two  equal  parts  between  the  poles,  is  called  the 
equator,  or  equinoctial  line  ;  that  part  of  the  globe  to 
the  north  of  the  equator  is  the  northern  hemisphere  ; 
that  part  to  the  south  of  the  equator,  the  southern 
Iiemisphere.  The  small  circle  E  F,  which  surrounds 
the  north  pole,  is  called  the  arctic  circle  ;  that  G  H, 
which  surrounds  the  south  pole,  the  antarctic  circle. 
There  are  two  intermediate  circles  between,  the 
polar  circles  and  the  equator;  that  to  the  north, 
I  K,  called  the  tropic  of  Cancer ;  that  to  the  souths 


110  OJJ  THE  EARTfir. 

L  M,  called  the  tropic  of  Capricorn.  Lastly,  thi 
circle,  L  K,  which  divides  the  globe  into  two  equal 
parts,  crossing  the  equator  and  extending  northward 
as  far  as  the  tropic  of  Cancer,  and  southward  as 
far  as  the  tropic  of  Capricorn,  is  called  the  ecliptic. 
The  delineation  of  the  ecliptic  on  the  terrestrial 
globe  is  not  without  danger  of  conveying  false  ideas  ; 
for  the  ecliptic  (as  I  have  before  said)  is  an  imagi- 
nary circle  in  the  heavens  passing  through  the  mid- 
dle of  the  zodiac,  and  situated  in  the  plane  of  the 
earth's  orbit. 

Caroline.  I  do  not  understand  the  meaning  of  the 
plane  of  the  earth's  orbit. 

Mrs.  D.  A  plane,  or  plain,  is  an  even  level  sur- 
face. Let  us  suppose  a  smooth  thin  solid  plain  cut- 
ting the  sun  through  the  centre,  extending  out  as  far 
as  the  tixed  stars,  and  terminating  in  a  circle  which 
passes  through  the  middle  of  the  zodiac  ;  in  this  plane 
the  earth  would  move  in  its  revolution  round  the  sun  ; 
it  is  therefore  called  the  plane  of  the  earth's  orbit, 
and  the  circle  in  which  this  plane  cuts  the  signs  of 
the  zodiac  is  the  ecliptic.  Let  the  fig.  1.  Plate  IX. 
represent  such  a  plane,  S  the  sun,  E  the  earth  with 
its  orbit,  and  A  B  C  D  the  ecliptic  passing  through  the 
middle  of  the  zodiac. 

Emily.  If  the  ecliptic  relates  only  to  the  heavens, 
why  is  it  described  upon  the  terrestrial  globe  ? 

Mrs.  B.  It  is  convenient  for  the  demonstration  of 
a  variety  of  problems  in  the  use  of  the  globes  ;  and 
besides,  the  obliquity  of  this  circle  to  the  equator  is 
rendered  more  conspicuous  by  its  being  described  on 
the  same  globe  ;  and  the  obliquity  of  the  ecliptic 
shows  the  inclination  of  the  earth's  axis  to  the  plane 
of  its  orbit.     But  to  return  to  fig.  2.  Plate  VIH. 

The  spaces  between  the  several  parallel  circles  on 
the  terrestrial  globe  are  called  zones  ;  that  which  is 
comprehended  between  the  tropics  is  distinguished  by 
the  name  of  the  torrid  zone  ;  the  spaces  which  ex- 
tend from  the  tropics  to  the  polar  circles,  the  north 


ON  THE  EARTH.  117 

and  south  temperate  zones  ;  and  the  spaces  contain- 
ed within  the  polar  circles,  the  frigid  zones.    . 

The  several  lines  which,  you  observe,  are  drawn 
from  one  pole  to  ihe  other,  cutting  the  equator  at 
right  angles,  are  called  meridians.  When  any  one  of 
these  meridians  is  exactly  opposite  the  sun  it  is  mid- 
day, or  twelve  o'clock  in  the  day,  with  all  the  places 
situated  on  that  meridian  ;  and,  with  the  places  situa- 
ted on  the  opposite  meridian,  it  is  consequently  mid- 
night. 

Emily.  To  places  situated  equally  distant  from 
these  two  meridians,  it  must  then  be  six  o'clock? 

Mrs.  B.  Yes  ;  if  they  are  to  the  east  of  the  sun's 
meridian  it  is  six  o'clock  in  the  afternoon,  because  the 
sun  will  have  previously  passed  over  them  ;  if  to  the 
west,  it  is  six  o'clock  in  the  morning,  and  the  sun  will 
be  {)roceeding  towards  that  meridian. 

Those  circles  which  divide  the  globe  into  two 
equal  parts,  such  as  the  equator  and  the  ecliptic,  are 
called  greater  circles  ;  to  distinguish  them  from  those 
which  divide  it  into  two  unequal  parts,  as  the  tropics 
and  polsyf  circles,  which  are  called  lesser  circles. 
All  circles  are  divided  into  360  equal  parts,  called  de- 
grees, and  degrees  into  60  equal  parts,  called  minutes. 
The  diameter  of  a  circle  is  a  right  line  drawn  across 
it,  and  passing  through  the  centre  ;  for  instance,  the 
boundary  of  this  sphere  is  a  circle,  and  its  axis  the  di- 
ameter of  that  circle  ;  the  diameter  is  equal  to  a  little 
less  than  one  third  of  the  circumference.  Can  you 
tell  me  nearly  how  many  degrees  it  contains  ? 

Caroline.  It  must  be  something  less  than  one  third 
of  360  degrees,  or  nearly  120  degrees. 

Mrs.  B.  Right  ;  now  Emily  you  may  tell  me 
exactly  how  many  degrees  are  contained  in  a  meri- 
dian ? 

Emily.  A  meridian,  reaching  from  one  pole  to  the 
other,  is  half  a  circle,  and  must  therefore  contain  180 
degrees. 

Mrs.  B.  Very  well :  and  what  number  of  degrees, 
are  there  from  the  equator  to  the  poles  ? 


118  ON  THE  EARTH. 

Caroline.  The  equator  being  equally  distant  iVom 
either  pole,  that  distance  must  be  half  ofa  meridian,  or 
a  quarter  of  the  circumference  ofa  circle,  and  con- 
tain 90  degrees. 

Mrs.  B.  Besides  the  usual  division  of  circles  into 
degrees,  the  ecliptic  is  divided  into  twelve  equal  parts, 
called  signs,  which  bear  the  names  of  the  constellations 
through  which  this  circle  passes  in  the  heavens. 
The  degrees  measured  on  the  meridians  from  north 
to  south,  or  south  to  north,  are  called  degrees  of  la- 
titude ;  those  measured  from  east  to  west  on  the 
equator,  the  ecliptic,  or  any  of  the  lesser  circles,  are 
called  degrees  of  longitude  ;  hence  these  circles 
bear  the  name  of  longitudinal  circles ;  they  are  also 
called  parallels  of  latitude. 

Emily.  The  degrees  of  longitude  must  then  vary 
in  length  according  to  the  dimensions  of  the  circle  on 
which  they  are  reckoned  ;  those,  for  instance,  at  the 
polar  circles  will  be  considerably  smaller  than  those 
at  the  equator  ? 

Mrs.  B.  Certainly  ;  since  the  degrees  of  circles 
of  different  dimensions  do  not  vary  in  number,  they 
must  necessarily  vary  in  length.  The  degrees  of  la- 
titude, you  may  observe,  never  vary  in  length  ;  for 
the  meridians  on  which  they  are  reckoned  are  all  of 
the  same  dimensions. 

Emily.     And  of  what  length  is  a  degree  of  latitude  ? 

Airs.  B.  Sixty  geographical  miles,  which  is  equal 
to  69i  English  statute  miles. 

Emily.  The  degrees  of  longitude  at  the  equator 
must  then  be  of  the  same  dimensions. 

Mrs.  B.  They  would,  were  the  earth  a  perfect 
sphere  ;  but  its  form  is  not  exactly  spherical,  being 
somewhat  protuberant  about  the  equator,  and  flat- 
tened towards  the  poles.  This  form  is  supposed  to 
proceed  from  the  superior  action  of  the  centrifugal 
power  at  the  equator. 

Caroline.  I  thought  I  had  understood  the  centri- 
fugal force  perfectly,  but  I  do  not  comprehend  its 
e£tect  in  this  instance. 


ON    THE    EARTH.  119 

Mrs.  B.  You  know  that  the  revolution  of  the 
earth  on  its  axis  must  give  every  particle  a  tenden- 
cy to  fly  o£F  from  the  centre,  that  this  tendency  is 
stronger  or  weaker  in  proportion  to  the  velocity  with 
which  the  particle  moves  ;  now  a  particle  situated 
near  one  of  the  polar  circles  makes  one  rotation  in 
the  same  space  of  time  as  a  particle  at  the  equator ; 
the  latter,  therefore,  having  a  much  larger  circle  to 
describe,  travels  proportionally  faster,  consequently 
the  centrifugal  force  is  much  stronger  at  the  equator 
than  at  the  polar  circles  :  it  gradually  decreases  as 
you  leave  the  equator  and  approach  the  poles,  where, 
as  there  is  no  rotatory  motion,  it  entirely  ceases. 
Supposing,  therefore,  the  earth  to  have  been  origi- 
nally in  u  fluid  state,  the  particles  in  the  torrid  zone 
would  recede  much  farther  from  the  centre  than 
those  in  the  frigid  zones  ;  thus  the  polar  regions 
would  become  flattened,  and  those  about  the  equator 
elevated. 

Caroline.  I  did  not  consider  that  the  particles  in 
the  neighbourhood  of  the  equator  move  with  greater 
velocity  than  those  about  the  poles  ;  this  was  the 
reason  I  could  not  understand  you. 

Mrs.  B.  You  must  be  careful  to  remember,  that 
those  parts  of  a  body  which  are  farthest  from  the 
centre  of  motion  must  move  with  the  greatest  velo- 
city :  the  axis  of  the  earth  is  the  centre  of  its  diur- 
nal motion,  and  the  equatorial  regions  the  parts  most 
distant  from  the  axis. 

Caroline.  My  head  then  moves  faster  than  my 
feet ;  and  upon  the  summit  of  a  mountain  we  are 
carried  round  quicker  than  in  a  valley  ? 

Airs.  B.  Certainly,  your  head  is  more  distant  from 
the  centre  of  motion  than  your  feet ;  the  mountain- 
top  than  the  valley  :  and  the  more  distant  any  part 
of  a  body  is  from  the  centre  of  motion,  the  larger  is 
the  circle  it  will  describe,  and  the  greater  therefore 
must  be  its  velocity. 

Emily.  I  have  been  reflecting,  that  if  the  earth  h 
not  a  perfect  circle 


120  ON    THE    EARTtt. 

Mrs.  B.  A  sphere  you  mean,  my  dear  ;  a  circle 
is  a  round  line,  every  part  of  which  is  equally  distant 
from  the  centre  ;  a  sphere  or  globe  is  a  round  body, 
the  surface  of  which  is  every  where  equally  distant 
from  the  centre. 

Emily.  If,  then,  the  earth  is  not  a  perfect  sphere, 
but  prominent  at  the  equator,  and  depressed  at  the 
poles,  would  not  a  body  weigh  heavier  at  the  equa- 
tor than  at  the  poles  ;  for  the  earth  being  thicker 
at  the  equator,  the  attraction  of  gravity  perpendicu- 
larly downwards  must  be  stronger. 

Mrs.  B.  Your  reasoning  has  some  plausibility,  but 
I  am  sorry  to,  be  obliged  to  add,  that  it  is  quite  er- 
roneous ;  for  the  nearer  any  part  of  the  surface  of  a 
body  is  to  the  centre  of  attraction,  the  more  strongly 
it  is  attracted  ;  because  the  most  considerable  quan- 
tity of  matter  is  about  that  centre.  In  regard  to  its 
effects,  you  might  consider  the  power  of  gravity  as 
that  of  a  magnet  placed  at  the  centre  of  attraction. 

Emily.  But  were  you  to  penetrate  deep  into  the 
earth,  would  gravity  increase  as  you  approached  the 
centre  ? 

Mrs.  B.  Certainly  not ;  1  am  referring  only  to 
any  situation  on  the  surface  of  the  earth.  Were 
you  to  penetrate  into  the  interior,  the  attraction  of  the 
parts  above  you  would  counteract  that  of  the  parts 
Ijeneatli  you,  and  consequently  diminish  the  power 
of  gravity  in  proportion  as  you  approached  the  cen- 
tre ;  and  if  you  reached  that  point,  being  equally 
attracted  by  the  parts  all  around  you,  gravity  would 
cease,  and  you  would  b^  without  weight. 

Emily.  Bodies  then  should  weigh  less  at  the 
equator  than  at  the  poles,  since  they  are  more  dis- 
tant from  the  centre  of  gravity  in  the  former  than  in 
the  latter  situation  ? 

Mrs.  B.  And  this  is  really  the  case  ;  but  the  dif- 
ference of  weight  would  be  scarcely  sensible,  were  it 
not  augmented  by  another  circumstance. 

Caroline.  And  what  is  this  singular  circumstance, 
which  seems  to  disturb  the  laws  of  nature  ? 


ON    THE    EARTH.  121 

Mrs,  B.  One  that  you  are  well  acquainted  with, 
as  conducing  more  to  the  preservation  than  the  de- 
struction of  order — the  centrifugal  force.  This  we 
have  just  observed  to  be  stronger  at  the  equator ;  and 
as  it  tends  to  drive  bodies  from  the  centre,  it  is  ne- 
cessarily opposed  to,  and  must  lessen  the  power  of 
gravity,  which  attracts  them  towards  the  centre. 
We  accordingly  find  that  bodies  weigh  lightest  at  the 
equator,  where  the  centrifugal  force  is  greatest ;  and 
heaviest  at  the  poles,  where  this  power  is  least. 

Carolinr.  Has  tlie  experiment  been  made  in  these 
different  situations  ? 

Mrs.  B,  Lewis  XIV.,  of  France,  sent  philosophers 
both  to  the  equator  and  to  Lapland  for  this  purpose  : 
the  severity  of  the  climate,  and  obstruction  of  the  ice, 
has  hitherto  rendered  every  attempt  to  reach  the 
pole  abortive ;  but  the  difference  of  gravity  at  the 
equator  and  in  Lapland  is  very  perceptible. 

Caroline,  Yet  I  do  not  comprehend,  how  the  dif- 
ference of  weight  could  be  ascertained ;  for  if  the 
body  under  trial  decreased  in  weight,  the  weight 
which  was  opposed  to  it  in  the  opposite  scale  must 
have  diminished  in  the  same  proportion.  For  in- 
stance, if  a  pound  of  sugar  did  not  weigh  so  heavy  at 
the  equator  as  at  the  poles,  the  leaden  pound  which 
served  to  weigh  it  would  not  be  so  heavy  either  ; 
therefore  they  would  still  balance  each  other,  and  the 
different  force  of  gravity  could  not  be  ascertained  by 
this  means. 

Mrs,  B,  Your  observation  is  perfectly  just :  the 
difference  of  gravity  of  bodies  situated  at  the  poles 
and  at  the  equator  cannot  be  ascertained  by  weigh- 
ing them ;  a  pendulum  was  therefore  used  for  that 
purpose. 

Caroline,  What,  the  pendulum  of  a  clock  ?  how 
could  that  answer  the  purpose  ? 

Mrs.  B.     A  pendulum  consists  of  a  line,  or  rod,  to 
one  end  of  which  a  weight  is  attached,  and  it  is  sus- 
pended by  the  other  to  a  fined  point,  about  which  it 
is  made  to  vibrate.     Without  being  put  in  motion,  a 
11 


122  ©N    THE    EARTHr 

pendulum,  like  a  plumb  line,  hangs  perpendicular  to 
the  general  surface  of  the  earth,  by  which  it  is  at- 
tracted ;  but,  if  you  raise  a  pendulum,  gravity  will 
bring  it  back  to  its  perpendicular  position.  It  will, 
however,  not  remain  stationary  there,  for  the  veloci- 
ty it  has  received  during  its  descent  will  impel  it  on- 
wards, and  it  will  rise  on  the  opposite  side  to  an  equal 
height ;  from  thence  it  is  brought  back  by  gravity,  and 
again  driven  by  the  impulse  of  its  velocity. 

Caroline.  If  so,  the  motion  of  a  pendulum  would 
be  perpetual,  and  1  thought  you  said,  that  there  was 
no  perpetual  motion  on  the  earth. 

Mrs.  B.  The  motion  of  a  pendulum  is  opposed 
by  the  resistance  of  the  air  in  which  it  vibrates,  and 
by  the  friction  of  the  part  by  which  it  is  suspended  : 
were  it  possible  to  remove  these  obstacles,  the  mo- 
tion of  a  pendulum  would  be  perpetual,  and  its  vi- 
brations perfectly  regular  ;  being  of  equal  distances, 
and  performed  in  equal  times. 

Emily.  That  is  the  natural  result  of  the  uniformi- 
ty of  the  power  which  produces  these  vibrations,  for 
the  force  of  gravity  being  always  the  same,  the  veloci- 
ty of  the  pendulum  must  consequently  be  uniform. 

Caroline.  No,  Emily,  you  are  mistaken  ;  the  cause 
is  not  always  uniform,  and  therefore  the  effect  will 
not  be  so  either.  I  have  discovered  it,  Mrs.  B.  ; 
since  the  force  of  gravity  is  less  at  the  equator  than 
at  the  poles,  the  vibrations  of  the  pendulum  will  be 
slower  at  the  equfitor  than  at  the  poles. 

Mrs.  B.  You  are  perfectly  right,  Caroline  ;  it 
was  by  this  means  that  the  difference  of  gravity  was 
discovered,  and  the  true  figure  of  the  earth  ascer- 
tained. 

Emily.  But  how  do  they  contrive  to  regulate 
their  time  in  the  equatorial  and  polar  regions  ?  for, 
since  in  this  part  of  the  earth  the  pendulum  of  a 
clock  vibrates  exactly  once  in  a  second,  if  it  vibrates 
faster  at  the  poles  and  slower  at  the  equator,  the 
inhabitants  must  regulate  their  clocks  in  a  different 
manner  frem  ours. 


ON   THE    EARTH.  133 

Mrs.  B.  The  only  alteration  required  is  to  length- 
en the  pendulum  in  one  case,  and  to  shorten  it  in  the 
other:  for  the  velocity  of  the  vibrations  of  a  pendu- 
lum depends  on  its  length  ;  and  when  it  is  said  that  a 
pendulum  vibrates  quicker  at  the  pole  than  at  the 
equator,  it  is  supposing  it  to  be  of  the  same  length. 
A  pendulum  which  vibrates  a  second  in  this  latitude 
is  36k  inches  long.  In  order  to  vibrate  at  the  equa- 
tor in  the  same  space  of  time,  it  must  be  lengthened 
by  the  addition  of  a  few  lines ;  and  at  the  poles,  it 
must  be  proportionally  shortened. 

I  shall  now,  I  think,  be  able  to  explain  to  you 
the  variation  of  the  seasons,  and  the  difference  of  the 
length  of  the  days  and  nights  in  those  seasons ;  both 
effects  resulting  from  the  same  cause. 

In  moving  round  the  sun,  the  axis  of  the  earth  is 
not  perpendicuhir  to  the  plane  of  its  orbit.  Suppo- 
sing this  round  table  to  represent  the  plane  of  the 
earth's  orbit,  and  this  little  globe,  which  has  a  wire 
passing  through  it,  representing  the  axis  and  poles, 
we  shall  call  the  earth  ;  in  moving  round  the  table, 
the  wire  is  not  perpendicular  to  it,  but  oblique. 

Emily.  Yes,  I  understand  the  earth  does  ftot  go 
round  the  sun  in  an  upright  position,  its  axis  is  slant- 
ing or  oblique. 

Mrs.  B.  All  the  lines,  which  you  learnt  in  your 
last  lesson,  are  delineated  on  this  little  globe  ;  you 
must  consider  the  ecliptic  as  representing  the  plane 
of  the  earth's  orbit;  and  the  equator,  which  crosses 
the  ecliptic  in  two  places,  shows  the  degree  of  obli- 
quity of  the  axis  of  the  earth  in  that  orbit,  which  is  ex- 
actly 23|  degrees.  The  points  in  which  the  ecliptic 
intersects  the  equator  are  called  nodes. 

But  I  believe  I  shall  make  this  clearer  to  you  by 
revolving  the  little  globe  round  a  candle,  which  shall 
represent  the  sun.     (Plate  IX.  6g.  2.) 

As  I  now  hold  it,  at  A,  you  see  it  in  the  situation  in 
which  it  is  in  the  midst  of  summer,  or  what  is  called 
the  summer  solstice,  which  is  on  the  Slst  of  June. 


1:24  ON    THE    EARTH. 

Emily.  You  hold  the  wire  awry,  I  suppose,  in  oi-- 
ier  to  show  that  the  axis  of  the  earth  is  not  upright '{ 

Mrs.  B.  Yes  ;  in  summer,  the  north  pole  is  incli- 
ned towards  the  sun.  In  this  season,  therefore,  the 
northern  hemisphere  enjoys  much  more  of  his  rays 
than  the  southern.  The  sun,  you  see,  now  shines 
over  the  whole  of  the  north  frigid  zone,  and  notwith- 
jstanding  the  earth's  diurnal  revolution,  which  I  imi 
tate  hy  twirling  the  ball  on  the  wire,  it  will  continue 
to  shine  upon  it  as  long  as  it  remains  in  this  situation, 
whilst  the  south  frigid  zone  is  at  tlie  same  time  com- 
pletely in  obscurity. 

Caroline.  That  is  very  strange  :  I  never  before 
heard  that  there  was  constant  day  or  night  in  any  part 
of  the  world!  Mow  mucli  happier  the  inhabitants  of 
the  north  frigid  zone  must  be  than  those  of  the  south- 
ern ;  the  first  enjoy  uninterrupted  day,  while  the 
last  are  involved  in  perpetual  darkness. 

Mrs.  B.  You  judge  with  too  much  precipitation  ; 
examine  a  little  further,  and  you  will  find,  that  the 
two  frigid  zones  share  an  equal  fate. 

We  shall  now  make  the  earth  set  off  from  its  posi- 
tion in  the  siimmer  solstice,  and  carry  it  round  the 
sun  ;  observe  that  the  pole  is  always  inclined  in  the 
same  direction,  and  points  to  the  same  spot  in  the 
heavens.  Tliere  is  a  fixed  star  situated  near  that 
spot,  which  is  hence  called  the  North  Polar  star. 
Now  let  us  stop  the  earth  at  B,  and  examine  it  in  its 
present  situation  ;  it  has  gone  through  one  quarter  of 
its  orbit,  and  is  arrived  at  that  point  at  which  the 
ecliptic  cuts  or  crosses  the  equator,  and  which  is  call- 
ed the  autumnal  equinox. 

Emily.     That  is  then  one  of  the  nodes. 

The  sun  now  shines  from  one  pole  to  the  other, 
just  as  it  would  constantly  do,  if  the  axis  of  the  earth 
were  perpendicular  to  its  orbit, 

Mrs.  B.  Because  the  inclination  of  the  axis  is  now 
neither  towards  the  sun  nor  in  the  contrary  direction  ; 
at  this  period  ef  the  year,  therefore,  the  days  and 
nights  are  equal  in  every  part  of  the  earth.     But  the 


UN    THE    EARTH.  1.25 

uext  Step  she  takes  in  her  orbit,  you  see,  involves  the 
north  pole  in  darkness,  whilst  it  illumines  that  of  the 
south  ;  this  change  was  gradually  preparing  as  1  mo- 
ved the  earth  from  summer  to  autumn  ;  the  arctic 
circle,  which  was  at  tirst  entirely  illumined,  began  to 
have  short  nights,  which  increased  as  the  earth  ap- 
proached the  autumnal  equinox;  and  the  instant  it 
passed  that  point,  the  long  night  of  the  north  pole 
commences,  and  the  south  pole  begins  to  enjoy  the 
light  of  the  sun.  We  shall  now  make  the  earth  pro- 
ceed in  its  orbit,  and  you  may  observe  that  as  it  ad- 
vances, the  days  shorten,  and  the  nights  lengthen, 
throughout  the  northern  hemisphere,  until  it  arrives 
at  the  winter  solstice^on  the  21st  of  December,  when 
the  north  frigid  zone  is  entirely  in  darkness,  and  the 
southern  has  uninterrupted  daylight. 

Caroline.  Then,  after  all,  the  sun,  which  I  thought 
so  partial,  confers  his  favours  equally  on  all. 

Mrs.  B.  Not  so  neither ;  the  inhabitants  of  the 
torrid  zone  have  much  more  heat  than  we  have,  aa 
the  sun's  rays  fall  perpendicularly  on  them,  while 
they  shine  obliquely  on  the  rest  of  the  world,  and  al- 
most horizontally  on  the  poles  ;  for  during  their  long 
day  of  six  months,  the  sun  moves  round  their  horizon 
without  either  rising  or  setting;  the  only  observable 
difference  is,  that  it  is  more  elevated  by  a  few  de- 
grees at  midday,  than  at  midnight. 

Emily.  To  a  person  placed  in  the  temperate  zone, 
in  the  situation  in  which  we  are  in  England,  the  sun 
will  shine  neither  so  obliquely  as  it  does  on  the  poles, 
nor  so  vertically  as  at  the  equator  ;  but  its  rays  will 
fall  upon  him  more  obliquely  in  autumn  and  winter, 
than  in  summer. 

Caroline.  And,  therefore,  the  inhabitants  of  the 
temperate  zones  will  not  have  merely  one  day  and 
one  night  in  the  year  as  happens  at  the  poles,  nor  will 
they  have  equal  days  and  equal  nights  as  at  the  equa- 
tor ;  but  their  days  and  nights  will  vary  in  length,  at 
different  times  of  the  year,  according  as  their  respec- 
tive poles  incline  towards  or  from  the  sun,  and  the 
11* 


JiG  ON    THE    EARTH. 

difference  will  be  greater  in  proportion  to  their  dis- 
tance  from  the  equator. 

Mrs.  B,  We  shall  now  follow  the  earth  through 
the  other  half  of  her  orbit,  and  you  will  observe,  that 
now,  exactly  the  same  effect  takes  place  in  the  south- 
ern hemisphere,  as  what  we  have  just  remarked  in 
the  northern.  Day  commences  at  the  south  pole 
when  night  sets  in  at  the  north  pole ;  and  in  every 
other  part  of  the  southern  hemisphere  the  days  are 
longer  than  the  nights,  while,  on  the  contrary,  our 
eights  are  longer  than  our  days.  When  the  earth  ar- 
rives at  the  vernal  equinox,  D,  where  the  ecliptic 
again  cuts  the  ei^uator,  on  the  26th  of  March,  she  is 
situated,  with  respect  to  the  sun,  exactly  in  the  same 
position  as  in  the  autumnal  equinox  ;  and  the  only 
difference  with  respect  to  the  earth  is,  that  it  is  now 
autumn  in  the  southern  hemisphere,  whilst  it  is  spring 
with  us. 

Caroline.  Then  the  days  and  nights  are  again 
every  where  equal  ? 

Mrs.  B.  Yes,  for  the  half  of  the  globe  which  is 
enlightened  extends  exactly  from  one  pole  to  the 
other ;  the  day  breaks  to  the  north  pole,  and  the  sun 
sets  to  the  south  pole  ;  but  in  every  other  part  of  the 
globe,  the  day  and  night  is  of  twelve  hours  length, 
hence  the  word  equinox,  which. is  derived  from  the 
Latin,  meaning  equal  night. 

As  the  earth  proceeds  towards  summer,  the  days 
lengthen  in  the  northern  hemisphere,  and  shorten  in 
the  southern,  till  the  earth  reaches  the  summer  sol- 
stice, when  the  north  frigid  zone  is  entirely  illumined, 
and  the  southern  is  in  complete  darkness  ;  and  we 
have  now  brought  the  earth  again  to  the  spot  from 
whence  we  tirst  accompanied  her. 

Emily.  This  is  indeed  a  most  satisf;\ctory  expla- 
nation of  the  seasons ;  and  the  more  I  learn,  the 
more  I  admire  the  simplicity  of  means  by  which  such 
wonderful  effects  are  produced. 

Mrs.  B.  1  know  not  which  is  most  worthy  of  our 
admiration,  the  cause,  or  the  effect  of  the  earth's  re» 


6N    THE    EARTH.  127 

Tolution  round  the  sun.  The  mind  can  find  no  ob- 
ject of  contemplation  more  sublime  than  the  course 
of  this  magnificent  globe,  impelled  by  the  combined 
powers  of  projection  and  attraction  to  roll  in  one  in- 
variable course  around  the  source  of  light  and  heat: 
and  what  can  be  more  delightful  than  the  beneficent 
effects  of  this  vivifying  power  on  its  attendant  planet. 
It  is  at  once  the  grand  principle  which  animates  and 
fecundates  nature. 

Emily.  There  is  one  circumstance  in  which  this 
little  ivory  globe  appears  to  me  to  differ  from  the 
earth  ;  it  is  not  quite  dark  on  that  side  of  it  which  is 
turned  from  the  candle,  as  is  the  case  with  the  earth 
when  neither  moon  nor  stars  are  visible. 

Mrs,  B.  This  is  owing  to  the  light  of  the  candle 
being  reflected  by  the  walls  of  the  room  on  every 
part  of  the  globe,  consequently  that  side  of  the  globe 
on  which  the  candle  does  not  directly  shine,  is  not  in 
total  darkness.  Now  the  skies  have  no  walls  to  re- 
flect the  sun's  light  on  that  side  of  our  earth  which  is 
in  darkness. 

Caroline.  I  beg  your  pardon,  Mrs.  B.,  I  think 
that  the  moon  and  stars  answer  the  purpose  of  walls 
in  reflecting  the  sun's  light  to  us  in  the  night. 

Mrs.  B.  Very  well,  Caroline ;  that  is  to  say,  the 
moon  and  planets  ;  for  the  fixed  stars,  you  know, 
shine  by  their  own  light. 

Emily.  You  say,  that  the  superior  heat  of  the 
equatorial  parts  of  the  earth  arises  from  the  rays 
falling  perpendicularly  on  those  regions,  whilst  they 
fall  obliquely  on  these  more  northern  regions  ;  now 
1  do  not  understand  why  perpendicular  rays  should 
afford  more  heat  than  oblique  rays. 

Caroline.  You  need  only  hold  your  hand  perpen- 
dicularly over  the  candle,  and  then  hold  it  sideways 
obliquely,  to  be  sensible  of  the  difference. 

Emily,  I  do  not  doubt  the  fact,  but  I  wish  to  have 
it  explained. 

Airs,  B.  You  are  quite  right ;  if  Caroline  had  not 
been  satisfied  with  ascertaining  the  fact,  without  u!>* 


5:^B  ON    THE    KAHTtf. 

derstanding  it,  she  would  not  have  brought  forward 
the  candle  as  an  illustration  j  the  reason  why  3'ou 
feel  so  much  more  heat  if  you  hold  your  hand  per- 
pendicularly over  the  candle,  than  if  you  hold  it  aide- 
ways,  is  because  a  stream  of  heated  vapour  constantly 
ascends  from  the  candle,  or  any  other  burning  body, 
which  being  lighter  than  the  air  of  the  room,  does 
not  spread  laterally  but  rises  perpendicularly,  and 
this  led  you  to  suppose  that  the  rays  were  hotter  in 
the  latter  direction.  Had  you  reflected,  you  would 
have  discovered  that  rays  issuing  from  the  candle 
sideways,  are  no  less  perpendicular  to  your  hand 
when  held  opposite  to  them,  than  the  rays  which  as- 
cend when  your  hand  is  held  over  them. 

The  reason  why  the  sun's  rays  afford  less  heat 
when  in  an  oblique  direction  than  when  perpendicu- 
lar, is  because  fewer  of  them  fall  upon  an  equal  por- 
tion of  the  earth ;  this  will  be  understood  better  by 
referring  to  Plate  X.  fig.  1,  which  represents  two 
equal  portions  of  the  sun's  rays,  shining  upon  difl'er- 
ent  parts  of  the  earth.  Here  it  is  evident,  that  the 
same  quantity  of  rays  fall  on  the  space  A  B,  as  fall 
on  the  space  B  C  ;  and  as  A  B  is  less  than  B  C,  the 
heat  and  light  will  be  much  stronger  in  the  former 
than  in  the  latter;  A  B,  you  see,  represents  the 
equatorial  regions,  where  the  sun  shines  perpendicu- 
larly ;  and  B  C,  the  temperate  and  frozen  climates, 
where  his  rays  fall  more  obliquely. 

Emily.  This  accounts  not  only  for  the  greater 
heat  of  the  equatorial  regions,  but  for  the  greater 
heat  of  summer  ;  as  the  sun  shines  less  obliquely  ia 
summer  than  in  winter. 

Airs.  B.     This  you  will  see  exemplified  in  figure 

-2,  in  which  the  earth  is  represented  as  it  is  situated 

*on  the  21st  of  June,  and  England  receives  less  oblique, 

and  consequently  a  greater  number  of  rays,  than  at 

any  other  season ;  and  figure  3,  shows  the  situation 

of  England  on  the  21st  of  December,  when  the  rays 

*of  the  sun  fall  most  obliquely  upon  her.     But  there 

-*#-  ako  another  reasoa  why  ..oblique  rays  give  le«s 


m.  J. 


Tiif-    4. 


ON    THE    EARTH*  123 

keat  than  perpendicular  rays ;  which  i^,  that  they 
have  a  greater  portion  of  the  atmosphere  to  traverse ; 
and  though  it  is  true  that  the  atmosphere  i«  itself  a 
transparent  body,  freely  admitting  the  passage  of  the 
sun's  rays,  yet  it  is  always  loaded  more  or  less  with 
dense  and  foggy  vapour,  which  the  rays  of  the  sun 
cannot  easily  penetrate  ;  therefore  the  greater  the 
quantity  of  atmosphere  the  sun's  rays  have  to  pass 
through  in  their  way  to  the  earth,  the  less  heat  they 
will  retain  when  they  reach  it.  'J'his  will  be  better 
\inderstood  by  rt^ferring  to  fig.  4.  The  dotted  line 
round  the  earth  describes  the  extent  of  the  atmos- 
phere, and  the  lines  which  proceed  from  the  sun  to 
the  earth  the  passage  of  two  equal  portions  of  the 
sun's  rays  to  the  equatorial  and  polar  regions  ;  the 
latter,  you  see,  from  its  greater  obliquity  passes 
through  a  greater  extent  of  atmosphere. 

Caroline.  And  this,  no  doubt,  is  the  reason  why 
the  sun  in  the  morning  and  the  evening  gives  so  much 
less  heat  than  at  midday. 

Mrs.  B.  The  diminution  of  heat,  morning  and 
evening,  is  certainly  owing  to  the  greater  obliquity 
of  the  sun's  rays  ;  and  as  such  they  are  affected  by 
both  the  causes  which  I  have  just  explained  to  you  ; 
the  difficulty  of  passing  through  a  foggy  atmosphere  is 
perhaps  more  particularly  applicable  to  them,  as 
mists  and  vapours  are  very  prevalent  about  the  time 
of  sunrise  and  sunset.  But  the  diminished  obliquity 
of  the  sun's  rays  is  not  the  sole  cause  of  the  heat  of 
summer  ;  the  length  of  the  days  greatly  conduces  to 
it ;  for  the  longer  the  sun  is  above  the  horizon,  the 
more  heat  he  will  communicate  to  the  earth. 

Caroline.  Both  the  longest  days,  and  the  most  per- 
pendicular rays,  are  on  the  21st  of  June  ;  and  yet  the 
greatest  heat  prevails  in  July  and  August. 

Mrs.  B.  Those  parts  of  the  earth  which  are  once 
heated,  retain  the  heat  for  some  length  of  time,  and 
the  additional  heat  they  receive,  occasions  an  eleva- 
tion of  temperature,  although  the  days  begin  to  short- 
en, and  the  sun's  rays  to  fall  more  obliquely.     For 


130  ©N    THE    EARTH. 

the  same  reason,  we  have  generally  more  heat  ai 
three  o'clock  in  the  afternoon,  than  at  twelve,  when 
the  sun  is  on  the  meridian. 

Emily.  And  pray,  have  the  other  planets  the  same 
vicissitudes  of  seasons  as  the  earth  ? 
-  Mrs.  B.  Some  of  them  more,  some  less,  accord- 
ing as  their  axes  deviate  more  or  less  from  the  per- 
pendicular to  the  plane  of  their  orbits.  The  axis  of 
Jupiter  is  nearly  perpendicular  to  the  plane  of  his  or- 
bit ;  the  axes  of  Mars  and  of  Saturn  are  each  inclined 
at  angles  of  about  sixty  degrees  ;  whilst  the  axis  of 
Venus  is  believed  to  be  elevated  only  fifteen  or  twenty 
degrees  above  her  orbit  ;  the  vicissitudes  of  her  sea- 
sons must  theretbre  be  considerably  greater  than 
ours.  For  further  particulars  respecting  the  planets, 
I  shall  refer  you  to  Bonnycastle's  Introduction  to 
Astronomy. 

1  have  but  one  more  observation  to  make  to  you 
relative  to  the  earth's  motion,  which  is,  that  although 
we  have  but  365  days  and  nights  in  the  year,  she  per- 
forms 366  complete  revolutions  on  her  axis  during 
that  time. 

Caroline.  How  is  that  possible  ?  for  every  com- 
plete revolution  must  bring  the  same  place  back  to 
the  sun.  It  is^novv  just  twelve  o'clock,  the  sun  is, 
therefore,  on  our  meridian  ;  in  twenty-four  hours 
will  it  not  be  returned  to  our  meridian  again,  and  will 
not  the  earth  have  made  a  complete  rotation  on  its 
axis  ? 

Mrs.  B.  If  the  earth  had  no  progressive  motion 
in  its  orbit  whilst  it  revolves  on  its  axis,  this  would 
be  the  case  ;  but  as  it  advances  almost  a  degree  west- 
ward in  its  orbit,  in  the  same  time  that  it  completes 
a  revolution  eastward  on  its  axis,  it  must  revolve 
nearly  one  degree  more  in  order  to  bring  the  same 
meridian  back  to  the  sun. 

Caroline.  Oh,  yes  !  it  will  require  as  much  more 
of  a  second  revolution  to  bring  the  same  meridian 
back  to  the  sun,  as  is  equal  to  the  space  the  earth 


ON   THE    EARTH.  131 

has  advanced  in  her  orbit,  that  is,  nearly  a  degree  ; 
this  difference  is,  however,  very  little. 

Mrs.  B.  These  small  daily  portions  of  rotation  are 
each  equal  to  the  three  hundred  and  sixty-fifth  part 
of  a  circle,  which  at  the  end  of  the  year  amounts  to 
one  complete  rotation. 

Emily.  That  is  extremely  curious.  If  the  earth, 
then,  had  no  other  than  its  diurnal  motion,  we  should 
have  366  days  in  the  year. 

Mrs  B.  We  should  have  366  days  in  the  same 
period  of  time  that  we  now  have  365  :  but  if  we  did 
not  revolve  round  the  sun,  we  should  have  no  na- 
tural means  of  computing  years. 

You  will  be  surprised  to  hear,  that  if  lime  is  calcu- 
lated by  the  stars  instead  of  the  sun,  the  irregularity 
which  we  have  just  noticed  does  not  occur,  and  that 
one  complete  rotation  of  the  earth  on  its  axis,  brings 
the  same  meridian  back  to  any  fixed  star. 

Emily.  That  seems  quite  unaccountable  ;  for  the 
earth  advances  in  her  orbit  with  regard  to  the  fixed 
stars,  the  same  as  with  regard  to  the  sun. 

Mrs.  B.  True,  but  then  the  distance  of  the  fixed 
stars  is  so  immense,  that  our  solar  system  is  in  com- 
parison to  it  but  a  spot,  and  the  whole  extent  of  the 
earth's  orbit  but  a  point  ;  therefore,  whether  the 
earth  remained  stationary,  or  whether  it  revolved  in 
its  orbit  durins;  its  rotation  on  its  axis,  no  sensible  dif- 
ference would  be  produced  with  regard  to  the  fixed 
stars.  One  complete  revolution  brings  the  same 
meridian  back  to  the  same  fixed  star  ;  hence  the  fix- 
ed stars  appear  to  go  round  the  earth  in  a  shorter 
time  than  the  sun  by  three  minutes  fifty-six  seconds 
of  time. 

Caroline.  These  three  minutes  fifty-six  seconds  is 
the  time  which  the  earth  takes  to  perform  the  addi- 
tional three  hundred  and  sixty-fifth  part  of  the  circle, 
in  order  to  bring  the  same  meridian  back  to  the  sun. 

Mrs.  B.  Precisely.  Hence  the  j^tars  gain  every 
<Jay  three  minutes  fifty-six  seconds  on  the  sun,  which 


13ii  »N    THK  EARTH. 

makes  them  rise  that  portion  of  time  earlier  erery 
day. 

When  time  is  calculated  by  the  stars  it  is  called 
sidereal  time,  when  by  the  sun  solar  or  apparent  time. 

Caroline.  Then  a  sidereal  day  is  three  minutes 
fifty-six  seconds  shorter  than  a  solar  day  of  twenty- 
four  hours. 

Mrs.  B.  I  must  also  explain  to  you  what  is  meant 
by  a  sidereal  year. 

The  common  year,  called  the  solar  or  tropical 
year,  containing  363  days,  five  hours,  forty-eight 
minutes,  and  fifty-two  seconds,  is  measured  from  the 
time  the  sun  sets  out  from  one  of  the  equinoxes,  or 
solstices,  till  it  returns  to  the  same  again  ;  but  this 
year  is  completed  before  the  earth  has  finished  one 
entire  revolution  in  its  orbit. 

Emily.  I  thought  that  the  earth  performed  one 
complete  revolution  in  its  orbit  every  year  ;  what  is 
the  reason  of  this  variation  ? 

Mrs.  B.  It  is  owing  to  the  spheroidal  figure  of  the 
earth.  The  elevation  about  the  equator  produces 
much  the  same  effect  as  if  a  similar  mass  of  matter, 
collected  in  the  form  of  a  moon,  revolved  round  the 
equator.  When  this  moon  acted  on  the  earth  in  con- 
junction with  or  in  opposition  to  the  sun,  variations 
in  the  earth's  motions  would  be  occasioned,  and  these 
variations  produce  what  is  called  the  precession  of 
the  equinoxes. 

Emily.  What  does  that  mean  ?  I  thought  the  equi- 
noctial points,  or  nodes,  were  fixed  points  in  the 
heavens,  in  which  the  equator  cuts  the  ecliptic. 

Mrs.  B.  These  points  are  not  quite  fixed,  but 
have  an  apparently  retrograde  motion,  that  is  to  say, 
instead  of  being  every  revolution  in  the  same  place, 
they  move  backwards.  Thus,  if  the  vernal  equinox 
is  at  A,  (fig.  1.  plate  XI.)  the  autumnal  one  will  be 
at  B  instead  of  C,  and  the  following  vernal  equinox 
at  D  instead  of  at  A,  as  would  be  the  case  if  the 
equinoxes  were  stationary  at  opposite  points  of  the 
earth's  orbit. 


PLATE  ja. 


©N  THE  EARTH.  13;^ 

Caroline.  So  that  when  the  earth  moves  from  one 
equinox  to  the  other,  though  it  takes  half  a  year  to 
perform  the  journey,  it  has  not  travelled  through 
half  its  orbit. 

Mrs.  B.  And,  consequently,  when  it  returns  again 
to  the  first  equinox,  it  has  not  completed  the  whole 
of  its  orbit.  In  order  to  ascertain  when  the  earth 
has  performed  an  entire  revolution  in  its  orbit,  we 
must  observe  when  the  sun  returns  in  conjunction 
with  any  fixed  star  ;  and  this  is  called  a  sidereal  year. 
Supposing  a  fixed  star  situated  at  E,  (fig.  1.  plate 
XI.)  the  sun  would  not  appear  in  conjunction  with 
it  till  the  earth  had  returned  to  A,  when  it  would 
have  completed  its  orbit. 

Emily.  And  how  much  longer  is  the  sidereal  than 
the  solar  year  ? 

Mrs.  B.  Only  twenty  minutes  ;  so  that  the  varia- 
tion of  the  equinoctial  points  is  very  inconsiderable. 
I  have  given  them  a  greater  extent  in  the  figure  in 
order  to  render  them  sensible. 

In  regard  to  time,  I  must  further  add,  that  the 
earth's  diurnal  motion  on  an  inclined  axis,  together 
with  its  annual  revolution  in  an  elliptic  orbit,  occa- 
sions so  much  complication  in  its  motion,  as  to  pro- 
duce many  irregularities  ;  therefore,  true  equal  time 
cannot  be  measured  by  the  sun.  A  clock,  which  was 
always  perfectly  correct,  would  in  some  parts  of  tlie 
year  be  before  the  sun,  and  in  other  parts  after  it. 
There  are  but  four  periods  in  which  the  sun  aud  a 
perfect  clock  would  agree,  which  is  the  16th  of 
April,  the  16th  of  June,  the  23d  of  August,  and  the 
24th  of  December. 

Emily.  And  is  there  any  considerable  difference 
between  solar  time  and  true  time  ? 

Mrs.  B.  The  greatest  difference  amounts  to  be- 
tween fifteen  and  sixteen  minutes.  Tables  of  equa- 
tion are  constructed  for  the  purpose  of  pointing  out 
and  correcting  these  differences  between  solar  time 
and  equal  or  mean  time,  which  is  the  denomination 
given  by  astronomers  to  true  time. 
12 


CONVERSATION  IX. 


ON  THE  MOON. 

Of  the  Mooii^s  Motion. — Phases  of  the  Moon. — Eclip- 
ses of  the  Moon. — Eclipses  of  Jupiter^s  Moons. — 
Of  the  Latitude  and  Longitude. — Of  the  Transits  of 
the  Inferior  Planets. — Of  the  Tides. 

MRS.  B.  We  shall  to-day  confine  our  attention  to 
the  moon,  which  offers  many  interesting  phenomena. 

The  moon  revolves  round  the  earth  in  the  space  of 
about  twenty-nine  days  and  a  half,  in  an  orbit  nearly 
parallel  to  that  of  the  earth,  and  accompanies  us  in 
our  revolution  round  the  sun. 

Emily.  Her  motion,  then,  must  be  rather  of  a 
complicated  nature  ;  for  as  the  earth  is  not  stationary, 
but  advances  in  her  orbit  whilst  the  moon  goes  round 
her,  the  moon  must  proceed  in  a  sort  of  progressive 
circle. 

Mrs.  B.  That  is  true  ;  and  there  are  also  other 
circumstances  which  interfere  with  the  simpUcity  and 
regularity  of  the  moon's  motion,  but  which  are  too 
intricate  for  you  to  understand  at  present. 

The  moon  always  presents  the  same  face  to  us,  by 
which  it  is  evident  that  she  turns  but  once  upon  her 
axis,  while  she  performs  a  revolution  round  the  earth; 
so  that  the  inhabitants  of  the  moon  have  but  one  day 
and  one  night  in  the  course  of  a  lunar  month. 

Caroline.  We  afford  them,  however,  the  advan- 
tage of  a  magnificent  moon  to  enlighten  their  long 
nights. 


ON    THE    MOON.  135 

Mrs.  B.  That  advantage  is  but  partial  ;  for  since 
we  always  see  the  same  hemisphere  of  the  moon,  the 
inhabitants  of  that  hemisphere  alone  can  perceive  us. 

Caroline,  One  half  of  the  moon  then  enjoys  our 
light  every  night,  while  the  other  half  has  constantly 
nights  of  darkness.  If  there  are  any  astronomers  in 
those  regions,  they  would  doubtless  be  tempted  to 
visit  the  other  hemisphere,  in  order  to  behold  so 
grand  a  luminary  as  we  must  appear  to  them.  But, 
pray,  do  they  see  the  earth  under  all  the  changes 
which  the  moon  exhibits  to  us  ? 

Mrs.  B.  Exactly  so.  These  changes  are  called 
the  phases  of  the  moon,  and  require  some  explana- 
tion. In  fig.  2,  plate  XI.  let  us  say  that  S  represents 
the  sun,  E  the  earth,  and  A  B  C  D  the  moon  in  dif- 
ferent parts  of  her  orbit.  When  the  moon  is  at  A, 
her  dark  side  being  turned  towards  the  earth,  we 
shall  not  see  her  as  at  a ;  but  her  disappearance  is  of 
very  short  duration,  and  as  she  advances  in  her  orbit 
we  perceive  her  under  the  form  of  a  new  moon  ; 
when  she  has  gone  through  one  eighth  of  her  orbit  at 
B,  one  quarter  of  her  enlightened  hemisphere  will 
be  turned  towards  the  earth,  and  she  will  then  appear 
horned  as  at  b:  when  she  has  performed  one  quarter 
of  her  orbit,  she  shows  us  one  half  of  her  enlighten- 
ed side  as  at  c ;  at  d  she  is  said  to  be  gibbous,  and  at 
e  the  whole  of  the  enlightened  side  appears  to  us, 
and  the  moon  is  at  full.  As  she  proceeds  in  her  or- 
bit she  becomes  again  gibbous,  and  her  enliglitened 
hemisphere  turns  gradually  away  from  us  till  she 
completes  her  orbit  and  disappears,  and  then  again 
resumes  her  form  of  a  new  moon. 

When  the  moon  is  at  full,  or  a  new  moon,  she  is 
said  to  be  in  conjunction  with  the  sun,  as  they  are 
then  both  in  the  same  direction  witli  regard  to  the 
earth  ;  when  at  her  quarters  she  is  said  to  be  in  op- 
position to  the  sun. 

Etnily.  Are  not  the  eclipses  produced  by  the  moon 
passing  between  the  sun  and  the  earth  ? 

Mrs.  B.  Yes  ;  when  the  moon  passes  between  the 
ftun  and  the  earth,  she  intercepts  his  rays,  or,  in  other 


136  ®N    THE    MOON. 

words,  casts  a  shadow  on  the  earth,  then  the  sun  is, 
eclipsed,  and  the  daylight  gives  phice  to  darkness, 
while  the  moon's  shadow  is  passing  over  us. 

When,  on  the  contrary,  the  earth  is  between  the 
sun  and  the  moon,  it  is  we  who  intercept  the  sun's 
rays,  and  cast  a  shadow  on  the  moon  ;  the  moon  is 
then  darkened,  she  disappears  from  our  view,  and 
is  eclipsed. 

Emily.  But  as  the  moon  goes  round  the  earth 
every  month,  she  must  be  once  during  that  time 
between  the  earth  and  the  sun,  and  the  earth  must 
likewise  be  once  between  the  sun  and  the  moon, 
and  yet  we  have  not  a  solar  and  a  lunar  eclipse  every 
month  ? 

Mrs.  B.  The  orbits  of  the  earth  and  moon  are 
not  exactly  parallel,  but  cross  or  intersect  each  other; 
and  the  moon  generally  passes  either  above  or  below 
the  earth  when  she  is  in  conjunction  with  the  sun, 
and  does  not  therefore  intercept  the  sun's  rays,  and 
produce  an  eclipse  ;  for  this  can  take  place  only  when 
the  earth  and  moon  are  in  conjunction  in  that  part  of 
their  orbits  which  cross  each  other,  (called  the  nodes 
of  their  orbits,)  because  it  is  then  only,  that  they  are 
both  in  a  right  line  with  the  sun. 

Emily.  And  a  partial  eclipse  takes  place,  I  sup- 
pose, when  the  moon,  in  passing  by  the  earth,  is  not 
sufficiently  above  or  below  the  earth's  shadow  en- 
tirely to  escape  it  ? 

Mrs.  B.  Yes,  one  edge  of  her  disk  then  dips  into 
the  shadow,  and  is  eclipsed  ;  but  as  the  earth  is 
larger  than  the  moon,  when  the  eclipse  happens 
precisely  at  the  nodes,  they  are  not  only  total,  but 
last  for  some  length  of  time. 

When  the  sun  is  eclipsed,  the  total  darkness  is 
confined  to  one  particular  part  of  the  earth,  evident- 
ly showing  that  the  moon  is  smaller  than  the  earth, 
since  she  cannot  entirely  skreen  it  from  the  sun.  In 
fig.  1,  pi.  XII.  you  will  find  a  solar  eclipse  describ- 
ed ;  S  is  the  sun,  M  the  moon,  and  E  the  earth  ;  and 
the  moon's  shadow,  you  see,  is  not  large  enough  to 


FLATS  JOI 


ON    THE    MOON,  1^7 

cover  the  earth.  The  lunar  eclipses,  on  the  contra- 
ry, are  visible  from  every  part  of  the  earth,  where 
the  moon  is  above  the  horizon  ;  and  we  discover,  by 
the  length  of  time  which  the  moon  is  in  passing 
through  the  earth's  shadow,  that  it  would  be  suffi- 
cient to  eclipse  her  totally,  were  she  47  times  her 
actual  size  ;  it  follows,  therefore,  that  the  earth  is 
47  times  the  size  of  the  moon. 

In  fig.  *£.  S  represents  the  sun,  which  pours  forth 
rays  of  light  in  straight  lines  in  every  direction.  E 
is  the  earth,  and  M  the  moon.  Now  a  ray  of  light 
coming  from  one  extremity  of  the  sun's  disk  in  the 
direction  A  B,  will  meet  another  coming  from  the  op- 
posite extremity  in  the  direction  C  B  ;  the  shadow  of 
the  earth  cannot  therefore  extend  beyond  B  ;  as  the 
sun  is  larger  than  the  earth,  the  shadow  of  the  latter 
is  conical,  or  the  figure  of  a  sugar  loaf ;  it  gradually 
diminishes,  and  is  much  smaller  than  the  earth  where 
the  moon  passes  through  it,  and  yet  we  find  the  moon 
to  be  not  only  totally  eclipsed,  but  some  length  of 
time  in  darkness,  and  hence  we  are  enabled  to  ascer- 
tain its  real  dimensions. 

Emily.  When  the  moon  eclipses  the  sun  to  us,  we 
must  be  eclipsed  to  the  moon  ? 

Mrs.  B.  Certainly;  for  if  the  moon  intercepts  the 
sun's  rays,  and  casts  a  shadow  on  us,  we  must  neces- 
sarily disappear  to  the  moon,  but  only  partially,  as  in 
fig.  1. 

Caroline  There  must  be  a  great  number  of  eclip- 
ses in  the  distant  planets,  which  have  so  many  moons  ? 

Mrs.  B.  Yes,  few  days  pass  without  an  eclipse 
taking  place  :  for  among  the  number  of  satellites,  one 
or  other  of  them  are  continually  passing  either  be- 
tween their  planet  and  the  sun,  or  between  the  planet 
and  each  other.  Astronomers  are  so  well  acquainted 
with  the  motion  of  the  planets  and  their  satellites,  that 
they  have  calculated  not  only  the  eclipses  of  our 
moon,  but  those  of  Jupiter,  with  such  perfect  accu- 
racy, that  it  has  aflbrded  a  means  of  aiscertaining  the 
longitude. 

12* 


138  ON  THE  MOON. 

Caroline.  But  is  it  not  very  easy  to  find  both  the 
latitude  and  longitude  of  any  place  by  a  map  or  globe  '. 

Mrs.  B  If  you  know  where  you  are  situated, 
there  is  no  difficulty  in  ascertaining  the  latitude  or 
longitude  of  the  place  by  referring  to  a  map  ;  but 
supposing  that  you  had  been  a  length  of  time  at  sea, 
interrupted  in  your  course  by  storms,  a  map  would 
afford  you  very  little  assistance  in  discovering  where 
you  were. 

Caroline.  Under  such  circumstances,  I  confess  I 
should  be  equally  at  a  loss  to  discover  either  latitude 
or  longitude. 

Mrs.  B.  The  latitude  may  be  easily  found  by  ta- 
king the  altitude  of  the  pole  ;  that  is  to  say,  the 
number  of  degrees  that  it  is  elevated  above  the  hori- 
zon, for  the  pole  appears  more  elevated  as  we  ap- 
proach it,  and  less  as  we  recede  from  it. 

Caroline.  But  unless  you  can  see  the  pole  how 
can  you  take  its  altitude  ? 

Mrs.  B.  The  north  pole  points  constantly  towards 
one  particular  part  of  the  heavens,  in  which  a  star 
is  situated,  called  the  Polar  Star  ;  this  star  is  visible  on 
clear  nights,  from  every  part  of  the  northern  hemis- 
phere; the  altitude  of  the  polar  star,  is  therefore  the 
same  number  of  degrees  as  that  of  the  pole  ;  the 
latitude  may  also  be  determined  by  observations  made 
on  the  sun  or  any  of  the  fixed  stars  ;  the  situation 
therefore  of  a  vessel  at  sea,  with  regard  to  north  and 
south,  is  easily  ascertained.  The  ditficulty  is  respect- 
ing east  and  west,  that  is  to  say,  its  longitude.  As  we 
have  no  eastern  poles  from  which  we  can  reckon  our 
distance,  some  particular  spot  must  be  fixed  upon 
for  that  purpose.  The  English  reckon  from  the 
meridian  of  Greenwich,  where  the  royal  observatory 
is  situated  ;  in  French  maps  you  will  find  that  the 
longitude  is  reckoned  from  Paris. 

The  rotation  of  the  earth  on  its  axis  in  24  hours 
iVom  west  to  east  occasions,  you  know,  an  apparent 
motion  of  the  sun  and  stars  in  the  contrary  direction, 
and  the  sun  appears  to  go  round  the  earth  in  the  space 


ON  THE  MOO-V.  139 

i)(  24  hours,  passing  over  fifteen  degrees,  or  a  twenty- 
fourth  part  of  the  earth's  circumference  every  hour; 
therefore,  when  it  is  twelve  o'clock  in  London,  it  is 
one  o'clock  in  any  place  situated  fifteen  degrees  to 
the  east  of  London,  as  the  sun  must  have  passed  the 
meridian  of  that  place  an  hour  before  he  reaches  that 
of  London.  For  the  same  reason  it  is  eleven  o'clock 
to  any  place  situated  fifteen  degrees  to  west  of  Lon- 
don, as  the  sun  will  not  come  to  that  meridian  till  an 
hour  later. 

If  then  the  captain  of  a  vessel  at  sea,  could  know 
precisely  what  was  the  hour  at  London,  he  could,  by 
looking  at  his  watch,  and  comparing  it  with  the  hour 
of  the  spot  in  which  he  was,  ascertain  the  longitude. 

Emily.  But  if  he  had  not  altered  his  watch,  since 
he  sailed  from  London,  it  would  indicate  the  hour  it 
was  then  in  London. 

Mrs.  B.  True  ;  but  in  order  to  know  the  hour  of 
the  day  of  the  spot  in  which  he  is,  the  captain  of  a 
vessel  regulates  his  watch  by  the  sun  when  it  reaches 
the  meridian. 

Emily.  Then  if  he  had  two  watches,  he  might 
keep  one  regulated  daily,  and  leave  the  other  unalter- 
ed ;  the  former  would  indicate  the  hour  of  the  place 
in  which  he  was  situated,  and  the  latter  the  hour  of 
London  ;  and  by  comparing  them  together,  he  would 
be  able  to  calculate  his  longitude. 

Mrs.  B.  You  have  discovered,  Emily,  a  mode  of 
finding  the  longitude,  which  I  have  the  pleasure  to 
tell  you,  is  universally  adopted  :  watches  of  a  supe- 
rior construction,  called  chronometers,  or  time-keep- 
ers, are  used  for  this  purpose  ;  but  the  best  watches 
are  liable  to  imperfections,  and  should  the  time-keep- 
er go  too  fast  or  too  slow,  there  would  be  no  means  of 
ascertaining  the  error  ;  implicit  reliance  cannot  con- 
sequently be  placed  upon  them. 

Recourse  is  therefore  had  to  the  eclipses  of  Jupi- 
ter's satellites.  A  table  is  made  of  the  precise  time 
at  which  the  several  moons  are  echpsed  to  a  specta- 
iov  at  London  j  when  they  appear  eclipsed  to  a  spec- 


140  ON  THE  MOON. 

tator  in  any  other  spot,  he  may,  by  consulting  the  ta- 
ble, know  what  is  the  hour  at  London  ;  for  the  eclipse 
is  visible  at  the  same  moment  from  whatever  place 
on  the  earth  it  is  seen.  He  has  then  only  to  look  at 
the  watch,  which  points  out  the  hour  of  the  place  Iq 
which  he  is,  and  by  observing  the  difference  of  time 
there,  and  at  London,  he  may  immediatel)'  determine 
his  longitude. 

Let  us  suppose,  that  a  certain  moon  of  Jupiter  is 
always  eclipsed  at  six  o'clock  in  the  evening  ;  and 
that  a  man  at  sea  consults  his  watch,  and  tinds  that  it 
is  ten  o'clock  at  ni^hi,  where  he  is  situated,  at  the 
moment  the  eclipse  takes  place  ;  what  will  be  big 
longitude  ? 

Emily.  That  is  four  hours  later  than  in  London  : 
four  times  fifteen  degrees  make  60  ;  he  would,  there- 
fore, be  sixty  degrees  east  of  London,  for  the  sun 
most  have  passed  his  meridian  before  it  reaches  that 
of  London. 

Mrs.  B.  For  this  reason  the  hour  is  always  later 
than  London,  when  the  place  is  east  longitude,  and 
earlier  when  it  is  west  longitude.  Thus  the  longitude 
can  be  ascertained  whenever  the  eclipses  of  Jupiter's 
moons  are  visible. 

But  it  is  not  only  the  secondary  planets  which  pro- 
duce eclipses,  for  the  primary  planets  near  the  sun 
eclipse  him  to  those  at  a  greater  distance  when  they 
come  in  conjunction  in  the  nodes  of  their  orbits  ;  but 
as  the  primary  planets  are  much  longer  in  performing 
their  course  round  the  sun,  than  the  satellites  in  going 
round  their  primary  planets,  these  eclipses  very  sel- 
dom occur. 

Mercury  and  Venus  have  however  passed  in  a 
right  line  between  us  and  the  sun,  but  being  at  so 
great  a  distance  from  us,  their  shadows  did  not  ex- 
tend so  far  as  the  earth  ;  no  darkness  was  therefore 
produced  on  any  part  of  our  globe  ;  but  the  planet 
appeared  like  a  small  black  spot,  passing  across  the 
sun's  disk  ;  this  is  called  a  transit  of  the  planet. 

It  was  by  the  last  transit  of  Venus,  that  astronO- 


ON  THE  MOON.  141 

mers  were  enabled  to  calculate  with  some  degree  of 
accuracy  the  distance  of  the  earth  from  the  sun,  and 
the  dimensions  of  the  latter. 

Emily.  1  have  heard  that  the  tiSes  are  affected 
by  the  moon,  but  I  cannot  conceive  what  influence  it 
can  have  on  them. 

Mrs.  B.  They  are  produced  by  the  moon's  at- 
traction, which  draws  up  the  waters  in  a  protu- 
berance. 

Caroline.  Does  attraction  act  on  water  more  pow- 
erfully than  on  land  ?  I  should  have  thought  it  would 
have  been  just  the  contrary,  for  land  is  certainly  a 
more  dense  body  than  water? 

Mrs.  B.  Tides  do  not  arise  from  water  bein^ 
more  strongly  attracted  than  land,  for  this  certainly  is 
not  the  case  ;  but  the  cohesion  of  fluids  being  much 
less  than  that  of  solid  bodies,  they  more  easily  yield 
to  the  power  of  gravity,  in  consequence  of  which 
the  waters  immediately  below  the  moon  are  drawn 
up  by  it  in  a  protuberance,  producing  a  full  tide,  or 
what  is  commonly  called  high  water,  at  the  spot 
where  it  happens.  So  far  the  theory  of  the  tides 
is  not  difficult  to  understand. 

Caroline.  On  the  contrary,  nothing  can  be  more 
simple  :  the  waters,  in  order  to  rise  up  under  the 
moon,  must  draw  the  waters  from  the  opposite  side 
of  the  globe,  and  occasion  ebb-tide,  or  low  water  in 
those  parts. 

Mrs.  B.  You  draw  your  conclusion  rather  too 
hastily,  my  dear  ;  for,  according  to  your  theory,  we 
should  have  full  tide  only  once  in  twenty-four  hours, 
that  is,  every  time  that  we  were  below  the  moon, 
%vhile  we  find  that  we  have  two  tides  in  the  course  of 
twenty-four  hours,  and  that  it  is  high-water  with  us 
and  with  our  antipodes  at  the  same  time. 

Caroline.  Yet  it  must  be  impossible  for  the  moon 
to  attract  the  sea  in  opposite  parts  of  the  globe,  and 
in  opposite  directions  at  the  same  time. 

Mrs.  B.  This  opposite  tide  is  rather  more  diffi- 
cult to  explain,  than  that  which  is  drawn  up  beneath 


142  ON  THE  MOON. 

the  moon  ;  with  a  little  attention,  however,  I  hope  I 
shall  be  able  to  make  you  understand  it. 

You  recollect  that  the  earth  and  moon  are  mutual- 
ly attracted  towards  a  point,  their  common  centre  of 
gravity  and  of  motion  ;  can  you  tell  me  what  it  is  that 
prevents  their  meeting  and  uniting  at  this  point  ? 

Emily.  Their  projectile  force,  which  gives  them  a 
tendency  to  fly  from  this  centre. 

Mrs.  B.  And  is  hence  called  their  centrifugal 
force.  Now  we  know  that  the  centrifugal  force  in- 
creases in  proportion  to  the  distance  from  the  centre 
of  motion. 

Caroline.  Yes,  I  recollect  your  explaining  that 
to  us,  and  illustrating  it  by  the  motion  of  the  flyers 
oi  a  wind-mill,  and  the  spinning  of  a  top. 

Emily.  And  it  was  but  the  other  day  you  showed 
us  that  bodies  weighed  less  at  the  equator  than  in  the 
polar  regions,  in  consequence  of  the  increased  cen- 
trifugal force  in  the  equatorial  parts. 

Mrs.  B.  Very  well.  The  power  of  attraction, 
on  the  contrary,  increases  as  the  distance  from  the 
centre  of  gravity  diminishes  ;  when,  therefore,  the 
two  centres  of  gravity  and  of  motion  are  in  the  same 
spot,  as  is  the  case  with  regard  to  the  moon  and  the 
earth,  the  centrifugal  power  and  those  of  attraction 
will  be  in  inverse  proportion  to  each  other  ;  that  is 
to  say,  where  the  one  is  strongest  the  other  will  be 
weakest. 

Emily.  Those  parts  of  the  ocean,  then,  which  are 
most  strongly  attracted,  will  have  least  centrifugal 
force  ;  and  those  parts  which  are  least  attracted,  will 
have  the  greatest  centrifugal  force. 

Mrs.  B.  In  order  to  render  the  question  more 
simple,  let  us  suppose  the  earth  to  be  every  where 
covered  by  the  ocean,  as  represented  in  fig.  S.  PI. 
XII.  M  is  the  moon,  ABC  D  the  earth,  and  X  the 
common  centre  of  gravity  and  of  motion  of  these 
two  planets.  Now  the  waters  on  the  surface  of  the 
earth,  about  A,  being  more  strongly  attracted  than 
any  other  part,  will  be  elevated  ;  the  attraction  of  the 


9N  THE  MOON.  143 

moon  at  B  and  C  being  less,  and  at  D  least  of  all. 
But  the  centrifugal  force  at  D  will  be  greatest,  and  the 
waters  there  will  in  consequence  have  the  greatest 
tendency  to  recede  from  the  moon  ;  the  waters  at  B 
and  C  will  have  less  tendency  to  recede,  and  at  A 
least  of  all.  The  waters,  therefore,  at  D,  will  re- 
cede furthest,  at  the  same  time  that  they  are  least  at- 
tracted, and  in  consequence  will  be  elevated  in  a  pro- 
tuberance similar  to  that  at  A. 

Emily.  The  tide  A,  then,  is  produced  by  the 
moon's  attraction,  and  increased  by  the  feebleness  of 
the  centrifugal  power  in  those  parts  ;  and  the  tide  D 
is  produced  by  the  centrifugal  force,  and  increased 
by  the  feebleness  of  the  moon's  attraction  in  those 
parts. 

Caroline.  And  when  it  is  high  water  at  A  and  D, 
it  is  low  water  at  B  and  C  :  now  I  think  I  compre- 
hend the  nature  of  the  tides  again,  though  1  confess 
it  is  not  quite  so  easy  as  I  at  first  thought. 

But,  Mrs.  B.,  why  does  not  the  sun  produce  tides 
as  well  as  the  moon  ;  for  its  attraction  is  greater  than 
that  of  the  moon  ? 

Mrs.  B.  It  would  be  at  an  equal  distance,  but  our 
vicinity  to  the  moon  makes  her  influence  more  pow- 
erful. The  sun  has,  however,  a  considerable  effect 
on  the  tides,  and  increases  or  diminishes  them  as  it 
acts  in  conjunction  with,  or  in  opposition  to  the  moon. 

Emily.     I  do  not  quite  understand  that. 

Mrs.  B.  The  moon  is  a  month  in  going  round  the 
earth  ;  twice  during  that  time,  therefore,  at  full  and 
at  change,  she  is  in  the  same  direction  as  the  sun,  both 
then  act  in  conjunction  on  the  earth,  and  produce 
very  great  tides,  called  spring  tides,  as  described  in 
fig.  4,  at  A  and  B  ;  but  when  the  moon  is  at  the  in- 
termediate parts  of  her  orbit,  the  sun,  instead  of  af- 
fording assistance,  weakens  her  power,  by  acting  in 
opposition  to  it  ;  and  smaller  tides  are  produced, 
called  neap  tides,  as  represented  in  fig.  5. 

Emily.  I  have  often  observed  the  difference  of 
these  tides  when  I  have  been  at  the  sea  side. 

But  fiince  attraction  is  mutual  between  the  moon 


144  •on  TflE  MOON. 

and  the  earth,  we  must  produce  tides  in  the  moon ; 
and  these  must  be  more  considerable  in  proportion  as 
our  planet  is  larejer.  And  yet  the  moon  does  not  ap- 
pear of  an  oval  form. 

Mrs.  B.  You  must  recollect,  that  in  order  to  ren- 
der the  explanation  of  the  tides  clearer,  we  supposed 
the  whole  surface  of  the  earth  to  be  covered  with  the 
ocean ;  but  that  is  not  really  the  case,  either  with 
the  earth  or  the  moon,  and  the  land  which  intersects 
the  water  destroys  the  regularity  of  the  effect. 

Caroline.  True ;  we  may,  however,  be  certain, 
that  whenever  it  is  high  water  the  moon  is  immediate- 
ly over  our  heads. 

Mrs.  B.  Not  so,  either;  for  as  a  similar  effect  is 
produced  on  that  part  of  the  globe  immediately  be- 
neath the  moon,  and  on  that  part  most  distant  from  it, 
it  cannot  be  over  the  heads  of  the  inhabitants  of  both 
those  situations  at  the  same  time.  Besides,  as  the 
orbit  of  the  moon  is  very  near'y  parallel  to  that  of 
the  earth,  she  is  never  vertical  but  to  the  inhabitants 
of  the  torrid  zone  ;  in  that  climate,  therefore,  the  tides 
are  greatest,  and  they  diminish  as  you  recede  from  it 
and  approach  the  poles. 

Caroline.  In  the  torrid  zone,  then,  I  hope  you 
will  grant  that  the  moon  is  immediately  over,  or  op- 
posite the  spots  where  it  is  high  water? 

Mrs.  B.  I  cannot  even  admit  that;  for  the  ocean 
naturally  partaking  of  the  earth's  motion,  in  its  rota- 
tion from  west  to  east,  the  moon,  in  forming  a  tide, 
has  to  contend  against  the  eastern  motion  of  the  waves. 
All  matter,  you  know,  by  its  inertia,  makes  some  re- 
sistance to  a  change  of  state ;  the  waters,  therefore, 
do  not  readily  yield  to  the  attraction  of  the  moon,  and 
the  effect  of  her  influence  is  not  complete  till  three 
hours  after  she  has  passed  the  meridian,  where  it  is 
full  tide. 

Emily.  Pray  what  is  the  reason  that  the  tid^  is 
three  quarters  of  an  hour  later  every  day? 

Mrs.  B.  Because  it  is  twenty-four  hours  and  three 
quarters  before  the  same  meridian  on  our  globe  re- 


OP  THE  MOON.  14i 

turns  beneath  the  moon.  The  earth  revolves  on  its 
axis  in  about  twenty-four  h^^urs ;  if  the  moon  were 
stationary,  therefore,  the  same  part  of  our  globe 
would,  every  twenty-four  hours,  return  beneath  the 
moon;  but  as  durinj;  our  daily  revolution  the  moon 
advances  in  her  orbit,  the  earth  must  make  more  than 
a  complete  rotation  in  order  to  brin^  the  same  meri- 
dian opposite  the  moon:  we  aie  three  quarters  of  an 
hour  in  overtaking  her.  The  tides,  therefore,  are 
retarded  for  the  same  reason  that  the  moon  rises  later 
by  three  quarters  of  an  hour  every  day. 

We  have  now,  I  think,  concluded  the  observations 
I  had  to  make  to  you  on  the  subject  of  astronomy ;  at 
<yur  next  interview,  I  shall  attempt  to  explain  to  you 
*he  elements  of  hydrostatics. 


13 


CONVERSATION  X. 


ON  THE  MECHANICAL  PROPERTIES 
OF  FLUIDS. 

Definition  of  a  Fluid. — Distinction  between  Fluids  and 
Liquids. — Of  JVon- Elastic  Fluids. — Scarcely  Suscep- 
tible of  Compression. — Of  the  Cohesion  of  Fluids. — 
Of  (heir  Gravitation. — Of  their  Equilibrium. — Of 
their  Pressure. — Of  Specific  Gravity. — Of  the  Speci- 
fic Gravity  of  Bodies  Heavier  than  Water. — Of  those 
of  the  Same  Weight  as  Water. — Of  those  Lighter  than 
Water, — Of  the  Specific  Gravity  of  Fluids. 

MRS.  B.  We  have  hitherto  confined  our  attention 
fo  the  noechanical  properties  of  solid  bodies,  which 
have  been  illustrated,  and,  1  hope,  thoroughly  im- 
pressed upon  your  memory,  by  the  conversations  we 
have  subsequently  had  on  astronomy.  It  will  now  be 
necessary  for  me  to  give  you  some  account  of  the  me- 
chanical properties  of  fluids — a  science  which  is  call- 
ed hydrostatics.  A  fluid  is  a  substance  which  yields 
to  the  slightest  pressure.  If  you  dip  your  hand  into 
a  basin  of  water,  you  are  scarcely  sensible  of  meeting 
with  any  resistance. 

Emily.  The  attraction  of  cohesion  is,  then,  I  sup- 
pose, less  powerfHl  in  fluids  than  in  solids  ? 

Airs.  B,  Yes  ;  fluids,  generally  speaking,  are  bo- 
dies of  less  density  than  solids.  From  the  slight  co- 
hesion of  the  particles  of  fluids,  and  the  facility  with 
which  they  slide  over  each  other,  it  is  inferred,  that 
they  must  be  small,  smooth,  and  globular;  smooth, 
beeause  there  appears  to  be  little  or  no  frictioB  among 


MECHANICAL  PROPERTIES  OF  FLUIDS.         147 

them,  and  globular,  because  touching  each  other  but 
by  a  point  would  account  for  the  slightness  of  their 
cohesion. 

Caroline.  Pray  what  is  the  distinction  between  a 
fluid  and  a  liquid  ? 

Mrs.  B.  Liquids  comprehend  only  one  class  of 
fluids.  There  is  another  class  distinguished  by  the 
name  of  elastic  fluids,  or  gases,  which  comprehends 
the  air  of  the  atmosphere,  and  all  the  various  kinds  of 
air  with  which  you  will  become  acquainted  when  you 
study  chemistry.  Tlieir  mechanical  properties  we 
shall  examine  at  our  next  meeting,  and  confine  our 
attention  this  morning  to  those  of  liquids,  or  non-elas- 
tic fluids. 

Water,  and  liquids  in  general,  are  scarcely  suscep- 
tible of  being  compressed,  or  squeezed  into  a  small- 
er space    than   that    which   they   naturally    occup3^ 
This  is  supposed  to  be  owing  to  the  extreme  minute- 
ness of  their  particles,  which,  rather  than  submit  to 
compression,  force  their  way  through  th^  pores  of 
the  substance  which  confines  them.     This  was  shown 
by  a  celebrated  experiment,  made  at  Florence  many 
.years  ago.      A  hollow  globe  of  gold  was  filled  with 
water,  and  on  its  being  submitted  to  great  pressure, 
the  water  was  seen  to  exude  through  the  pores  of 
the  gold,  which  it  covered  with  a  fine  dew.     Fluids 
gravitate  in  a  more  perfect  manner  than  solid  bodies  ; 
for  the  strong  cohesive  attraction  of  the  particles  of 
the  latter  in  some  measure  counteracts  the  eff"ect  of 
gravity.     In  this  table,  for  instance,  the  cohesion  of 
the   particles  of  wood   enables  four  slender  legs  to 
support  a  considerable  weight.      Were  the  cohesion 
destroyed,  or,  in  other  words,  the  wood  converted 
into  a  fluid,  no  support  could  be  afl'orded  by  the  legs, 
for  the  particles  no  longer  cohering  together,  each 
would  press  separately  and  independently,  and  would 
be  brought  to  a  level  with  the  surface  of  the  earth. 

Emily.  This  want  of  cohesion  is  then  the  rea- 
son why  fluids  can  never  be  formed  into  figures,  or 
maintained  in  heaps  ;  for  though  it  is  true  the  wind 


i48         MECHANICAL  PROPERTIES  OF  FLUIDS. 

raises  water  into  waves,  they  are  immediately  after- 
wards destroyed  by  gravity,  and  water  always  finds 
its  level. 

Mrs.  B,  Do  you  understand  what  is  meant  by  the 
level,  or  equilibrium  of  fluids  ? 

Emily.  I  believe  1  do,  though  I  feel  rather  at  a 
loss  to  explain  it.  Is  not  a  fluid  level  when  its  sur- 
face is  smooth  and  flat,  as  is  the  case  with  all  fluids 
when  in  a  state  of  rest  ? 

Mrs.  B.  Smooth,  if  you  please,  but  not  flat;  for 
the  definition  of  the  equilibrium  of  a  fluid  is,  that 
every  part  of  the  surface  is  equally  distant  from  the 
point  to  which  gravity  tends,  that  is  to  say,  from  the 
centre  of  the  earth  ;  hence  the  surface  of  all  fluids 
must  be  bulging,  not  flat,  since  they  will  partake  of 
the  spherical  form  of  the  globe.  This  is  very  evi- 
dent in  large  bodies  of  water,  such  as  the  ocean,  but 
the  sphericity  of  small  bodies  of  water  is  so  trifling, 
that  their  surfaces  appear  flat. 

This  level,  or  equilibrium  of  fluids,  is  the  natural 
result  of  their  particles  gravitating  independently  of 
each  other  ;  for  when  any  particle  of  a  fluid  acci- 
dentally finds  itself  elevated  above  the  rest,  it  is  at- 
tracted down  to  the  level  of  the  surface  of  the  fluid, 
and  the  readiness  with  which  fluids  yield  to  the 
slightest  impression,  will  enable  the  particle  by  its 
weight  to  penetrate  the  surface  of  the  fluid  and  mix 
with  it. 

CaroUnf.  But  I  have  seen  a  drop  of  oil  float  ob 
the  surface  of  water  without  mixing  with  it. 

Mrs,  B.  That  is,  because  oil  is  a  lighter  liquid 
than  water.  If  you  were  to  pour  water  over  it,  the 
oil  would  rise  to  the  surface,  being  forced  up  by  the 
superior  gravity  of  the  water.  Here  is  an  instru- 
ment called  a  water-level,  (fig.  1.  plate  XIII.)  which 
is  constructed  upon  the  principle  of  the  equilibrium 
of  fluids.  It  consists  of  a  short  tube,  A  B,  closed  at 
both  ends,  and  containing  a  little  water  ;  when  the 
tube  is  not  perfectly  horizontal  the  water  runs  to  the 
lower  end,  and  it  is  by  this  means  that  the  level  of 


Fi:if.  s. 


PLATE.  Xm. 


MECHANICAL  PROPERTIES  Or  FLUIDS.         149 

any  situation,  to  which  we  apply  the  instrument,  is 
ascertained. 

SoHd  bodies  you  may,  therefore,  consider  as  gra- 
vitating in  masses,  for  the  strong  cohesion  of  their 
particles  makes  them  weigh  altogether,  while  every 
particle  of  a  fluid  may  be  considered  as  composing 
a  separate  mass,  gravitating  independently  of  each 
other.  Hence  the  resistance  of  a  fluid  is  considera- 
bly less  than  that  of  a  solid  body  ;  for  the  resistance 
of  the  particles  acting  separately,  they  are  more 
easily  overcome. 

Emily.  A  body  of  water,  in  falling,  does  certainly 
less  injury  than  a  solid  body  of  the  same  weight. 

Mrs.  B.  The  particles  of  fluids  acting  thus  inde- 
pendently, press  against  each  other  in  every  direc- 
tion, not  only  downwards  but  upwards,  and  laterally 
or  sideways  ;  and  in  consequence  of  this  equality  of 
pressure,  every  particle  remains  at  rest  in  the  fluid. 
If  you  agitate  the  fluid  you  disturb  this  equality  of 
pressure,  and  the  fluid  will  not  rest  till  its  equili- 
brium is  restored. 

Caroline.  The  pressure  downwards  is  very  natu- 
ral ;  it  is  the  effect  of  gravity,  one  particle  weighing 
upon  another  presses  on  it ;  but  the  pressure  side- 
ways, and  particularly  the  pressure  upwards,  I  can- 
not understand. 

Mrs.  B.  If  there  were  no  lateral  pressure,  water 
would  not  run  out  of  an  opening  on  the  side  of  a 
vessel.  If  you  fill  a  vessel  with  sand,  it  will  not  run 
out  of  such  an  opening,  because  there  is  scarcely 
any  lateral  pressure  among  its  particles. 

Emily.  When  water  runs  out  of  the  side  of  a  ves- 
sel, is  it  not  owing  to  the  weight  of  the  water  above 
the  opening  ? 

Mrs.  B.  If  the  particles  of  fluids  were  arranged 
in  regular  columns  thus,  (fig.  2,)  there  would  be  no 
lateral  pressure,  for  when  one  particle  is  perpen- 
dicularly above  the  other,  it  can  only  press  it  down- 
wards ;  but  as  it  must  continually  happen,  that  a  par- 
ticle presses  between  two  particles  beneath,  (fig.  3,) 
these  last  must  suffer  a  lateral  pressure. 
13* 


150        MECHANICAL  PROPERTIES  OF  FLtJIDSf. 

Emily.  The  same  as  when  a  wedge  is  driven  into 
a  piece  of  wood,  and  separates  the  parts  laterally, 

Mrs.  B.  Yes.  The  lateral  pressure  proceeds, 
therefore,  entirely  from  the  pressure  downwards,  or 
the  weight  of  the  liquid  above  ;  and  consequently 
the  lower  the  orifice  is  made  in  the  vessel,  the  great- 
er will  be  the  velocity  of  the  water  rushing  out  of  it. 
Here  is  a  vessel  of  water  (fig.  4)  with  three  stop 
cocks  at  different  heights  ;  we  shall  open  them,  and 
you  will  see  with  what  different  degrees  of  velocity 
the  water  issues  from  them.  Do  you  understand 
this,  Caroline  ? 

Caroline.  Oh,  yes.  The  water  from  the  upper 
spout  receiving  but  a  slight  pressure,  on  account  of 
its  vicinity  to  the  surface,  flows  but  gently  ;  the 
second  cock  having  a  greater  weight  above  it,  the 
water  is  forced  out  with  greater  velocity,  whilst  the 
lowest  cock,  being  near  the  bottom  of  the  vessel,  re- 
ceives the  pressure  of  almost  the  whole  body  of  wa- 
ter, and  rushes  out  with  the  greatest  impetuosity. 

Mrs.  B.  Very  well :  and  you  must  observe,  that 
as  the  lateral  pressure  is  entirely  owing  to  the  pres- 
sure downwards,  it  is  not  effected  by  the  horizontal 
dimensions  of  the  vessel,  which  contains  the  water, 
but  merely  by  its  depth  ;  for  as  every  particle  acts 
independently  of  the  rest,  it  is  only  the  column  of 
*j)articles  immediately  above  the  orifice  that  can  weigh 
upon  and  press  out  the  water. 

Emily.  The  breadth  and  width  of  the  vessel  then 
oun,  be  of  no  consequence  in  this  respect.  The  late- 
ral pressure  on  one  side,  in  a  cubical  vessel,  is,  I  sup- 
pose, not  so  great  as  the  pressure  downwards. 

Mrs.  B.  No  :  in  a  cubical  vessel,  the  pressure 
downwards  will  be  double  the  lateral  pressure  on 
one  side  ;  for  every  particle  at  the  bottom  of  the 
vessel  is  pressed  upon  by  a  column  of  the  whole 
depth  of  the  fluid,  whilst  the  lateral  pressure  dimi- 
nishes from  the  bottom  upwards  to  the  surface,  where 
the  particles  have  no  pressure. 

Caroline,    A:»d  from  whence  proceeds  the  pr€£- 


MECHANICAL  PROPERTIES  OP  FLUIDS.        161 

sure  of  fluids  upwards  ?  that  seems  to  me  the  most 
unaccountable,  as  it  is  in  direct  opposition  to  gravity. 

Mrs.  B.  And  yet  it  is  a  consequence  of  their 
pressure  downwards.  When,  for  example,  you  pour 
water  into  a  tea-pot,  the  water  rises  in  the  spout  to 
a  level  with  the  water  in  the  pot.  The  particles  of 
water  at  the  bottom  of  the  pot  are  pressed  upon  by 
the  particles  above  them  ;  to  this  pressure  they  will 
yield,  if  there  is  any  mode  of  making  way  for  th© 
superior  particles,  and  as  they  cannot  descend,  they 
will  change  their  direction  and  rise  in  the  spout. 

Suppose  the  tea-pot  to  be  filled  with  columns  of  par- 
ticles of  water  similar  to  that  described  in  fig.  4.  the 
particle  1  at  the  bottom  will  be  pressed  laterally  by 
the  particle  2,  and  by  this  pressure  be  forced  into  the 
spout,  where,  meeting  with  the  particle  3,  it  presses 
it  upwards,  and  this  pressure  will  be  continued,  from 
3  to  4,  from  4  to  3,  and  so  on,  till  the  water  in  the 
spout  has  risen  to  a  level  with  that  in  the  pot. 

Emily,  if  it  were  not  for  this  pressure  upwards, 
forcing  the  water  to  rise  in  the  spout,  the  equilibrium 
of  the  fluid  would  be  destroyed. 

Caroline.  True  ;  but  then  the  tea-pot  is  wide  and 
large,  and  the  weight  of  so  great  a  body  of  water  as 
the  pot  will  contain,  may  easily  force  up  and  support 
so  small  a  quantity  as  will  fill  the  spout.  But  would 
the  same  effect  be  produced  if  the  spout  and  the  pot 
were  of  equal  dimensions  ? 

Mrs.  B.  Undoubtedly  it  would.  You  may  even 
reverse  the  experiment  by  pouring  water  into  the 
spout,  and  you  will  find  that  the  water  will  rise  in  the 
pot  to  a  level  with  that  in  the  spout ;  for  the  pressure 
of  the  small  quantity  of  water  in  the  spout  will  force 
up  and  support  the  larger  quantity  in  the  pot.  In  the 
pressure  upwards,  as  well  as  that  laterally,  you  see 
that  the  force  of  pressure  depends  entirely  on  the 
height,  and  is  quite  independent  of  the  horizontal 
dimensions  of  the  fluid. 

As  a  tea-pot  is  not  transparent,  let  us  try  the  ex- 
periment by  filling  this  large  glass  goblet  by  means 
of  this  narrow  tube.  (fig.  6.) 


152        MECHANICAL  PROPERTIES  OF  FLUIDS. 

Caroline.  Look,  Emily,  as  Mrs.  B.  fills  it,  how  the 
water  rises  in  the  goblet,  to  maintain  an  equilibrium 
with  that  in  the  tube. 

Now,  Mrs.  B.,  will  you  let  me  fill  the  tube  by  pour- 
ing water  into  the  goblet  ? 

Mrs.  B.  That  is  impossible.  However,  you  may 
try  the  experiment,  and  I  donbt  not  but  that  .you  will 
be  able  to  account  for  its  failure. 

Caroline.  It  is  very  sins^ular,  that  if  so  small  a 
column  of  water  as  is  contaim^d  in  the  tube  can  force 
up  and  support  the  whole  contents  of  the  goblet,  that 
the  weight  of  all  the  w  iter  in  the  goblet  should  not 
be  able  to  force  up  the  small  quantity  required  to  fill 
the  tube  : — oh,  I  see  now  the  reason,  water  in  the 
goblet  cannot  force  that  in  the  tube  above  its  level, 
and  as  the  end  of  the  tube  is  considerably  higher  than 
the  goblet,  it  can  never  be  filled  by  pouring  water  in- 
to the  goblet. 

Airs.  B.  And  if  you  continue  to  pour  water  into 
the  goblet  when  it  is  full,  the  water  will  run  over  in- 
stead of  rising  above  the  level  in  the  tube. 

I  shall  now  explain  to  you  the  meaning  of  the  spe- 
cific grarity  of  bodies. 

Caroline.  What !  is  there  another  species  of  gravi- 
ty with  which  we  are  not  yet  acquainted  ? 

Airs.  B.  No  ;  the  specific  gravity  of  a  body  means 
simply  its  weight  compared  with  that  of  another 
body  of  the  same  size.  When  we  say,  that  substances 
such  as  lead  and  stones  are  heavy,  and  that  others, 
such  as  paper  and  feathers,  are  light,  we  speak  compara- 
tively ;  that  is  to  say,  that  the  first  are  heavy,  and  the 
latter  light  in  comparison  with  the  generality  of  sub- 
stances in  nature.  Would  you  call  wood  and  chalk 
light  or  heavy  bodies  ? 

Caroline,  Some  kinds  of  wood  are  heavy  certain- 
ly, as  oak  and  mahogany  ;  others  are  light,  as  deal 
and  box. 

Emily.  I  think  I  should  call  wood  in  general  a 
heavy  body,  for  deal  and  box  are  light  only  in  com- 
parison to  wood  of  a  heavier  description.     I  am  at  a 


MECHANICAL  PROPERTIES  OP  FLUIDS.         153 

loss  to  determine  whether  chalk  should  be  ranked  as 
a  heavy  or  a  light  body;  I  should  be  inclined  to  say  the 
former,  if  it  was  not  that  it  is  lighter  than  most  other 
minerals.  I  perceive,  that  we  have  but  vague  notions 
of  light  and  heavy.  I  wish  there  was  some  standard 
of  comparison,  to  which  we  could  refer  the  weight 
of  all  other  bodies. 

A/rs.  B.  The  necessity  of  such  a  standard  has  been 
so  much  felt,  that  a  body  has  been  fixed  upon  for  this 
purpose.  What  substance  do  you  think  would  be 
best  calculated  to  answer  this  end  ? 

Caroline,  It  must  be  one  generally  known  and 
easily  obtained,  lead  or  iron,  for  instance. 

Mrs.  B.  All  the  metals  expand  by  heat,  and  con- 
dense by  cold.  A  piece  of  lead,  let  us  say  a  cubic 
inch  for  instance,  would  have  less  specific  gravity  in 
summer  than  in  winter  ;  for  it  would  be  more  dense 
in  the  latter  season. 

Caroline.  But,  Mrs.  B.,  if  you  compare  the  weight 
of  equal  quantities  of  difforcnt  bodies,  they  vv ill  all 
be  alike.  You  know  the  old  saying,  that  a  pound  of 
feathers  is  as  heavy  as  a  pound  of  lead  ? 

Mrs.  B.  When  therefore  we  compare  the  weight 
of  different  kinds  of  bodies,  it  would  he  absurd  to  take 
quantities  of  equal  weight,  we  must  take  quantities  of 
equal  bulk;  pints  or  quarts,  not  ounces  or  pounds. 

Caroline.  Very  true  ;  I  perplexed  myself  by  think- 
ing that  quantity  referred  to  weight,  rather  than  to 
measure.  It  is  true,  it  would  be  as  absurd  to  com- 
pare bodies  of  the  same  size  in  order  to  ascertain 
which  was  largest,  as  to  compare  bodies  of  the  same 
weight  in  order  to  discover  which  was  heaviest. 

Mrs.  B.  In  estimating  the  specific  gravity  of  bo- 
dies, therefore,  we  must  compare  equal  bulks,  and 
we  shall  find  that  their  specific  gravity  will  be  pro- 
portional to  their  weights.  The  body  which  has 
been  adopted  as  a  standard  of  reference  is  distilled 
water. 

Emily.  I  am  surprised  that  a  fluid  should  have 
been  chosen  for  this  purpose,  as  it  must  necessarily 


154         MECHANICAL  PROPERTIES  OF  FLUIDS. 

be  contained  in  some  vessel,   and  the  weight  of  the 
vessel  will  require  to  be  deducted. 

Mrs.  B.  In  order  to  learn  the  specific  gravity  of 
a  solid  body,  it  is  not  necessary  to  put  a  certain  mea- 
sure of  it  in  one  scale,  and  an  equal  measure  of  water 
into  the  other  scale  ;  but  simply  to  weigh  the  body 
under  trial  in  water.  If  you  weigh  a  piece  of  gold 
in  a  glass  of  water,  will  not  the  gold  displace  just  as 
much  water,  as  is  equal  to  its  own  bulk. 

Caroline.  Certainly,  where  one  body  is,  another 
cannot  be  at  the  same  time  ;  so  that  a  sufficient 
quantity  of  water  must  be  removed,  in  order  to  make 
way  for  the  gold. 

Mrs.  B.  Yes,  a  cubic  inch  of  water  to  make  room 
for  a  cubic  inch  of  gold  ;  remember  that  the  bulk 
alone  is  to  be  considered,  the  weight  has  nothing  to 
do  with  the  quantity  of  water  displaced,  for  an  inch 
of  gold  does  not  occupy  more  space,  and  therefore 
will  not  displace  more  water  than  an  inch  of  ivory, 
or  any  other  substance,  that  will  sink  in  water^ 

Well,  you  will  perhaps  be  surprised  to  hear  that  the 
gold  will  weigh  less  in  water,  than  it  did  out  of  it. 

Emily.     And  for  what  reason  ? 

Mrs.  B.  On  acronnt  of  the  upward  pressure  of  the 
particles  oi  water,  which  in  some  measure  supports 
the  gold,  and,  by  so  doing,  diminishes  its  weight.  If 
the  body  immersed  in  water  was  of  the  same  weight 
as  that  fluid,  it  would  be  wholly  supported  by  it, 
just  as  the  water  which  it  displaces  was  supported 
previous  to  its  making  way  for  the  solid  body.  If 
the  body  is  heavier  than  the  water,  it  cannot  be 
wholly  supported  by  it ;  but  the  water  will  offer 
some  resistance  to  its  descent. 

Caroline.  And  the  resistance  which  water  offers 
to  the  descent  of  heavy  bodies  immersed  in  it,  (since 
it  proceeds  from  the  upward  pressure  of  the  parti- 
cles of  the  fluid,)  must  in  all  cases,  1  suppose,  be  the 
same  ? 

Mrs.  B.  Yes  ;  the  resistance  of  the  fluid  is  pro- 
portioned to  the  bulk,  and  not  to  the  weight  of  the 


MECHANICAL  PROPERTIES  OP  FLUIDS.       155 

body  immersed  in  it ;  all  bodies  of  the  same  size, 
therefore,  lose  the  same  quantity  of  their  weight  in 
water.  Can  you  form  any  idea  what  this  loss  will 
be? 

Emily.  I  should  think  it  would  be  equal  to  the 
weii^ht  of  the  water  displaced  ;  for,  since  that  por- 
tion of  the  water  was  supported  before  the  immer- 
sion of  the  solid  body,  an  equal  weight  of  the  solid 
body  will  be  supported. 

Mrs.  B.  You  are  perfectly  rioht ;  a  body  weighed 
in  water  loses  just  as  much  of  its  weit^ht,  as  is  equal 
to  that  of  the  water  it  displaces  ;  so  that  if  you  were 
to  put  the  water  displaced  into  the  scale  to  vvliich  the 
body  is  suspended,  it  would  restore  the  balance. 

You  must  observe,  that  when  you  weig;h  a  body 
in  water,  in  order  to  ascertain  its  sperilic  gravity, 
you  must  not  sink  the  basin  of  the  balance  in  the 
water  ;  but  either  suspend  the  body  to  a  hook  at 
the  bottom  of  the  basin,  or  else  take  off  the  basin, 
and  suspend  it  to  the  arm  of  the  balance,  (fii?.  7.) 
Now  suppose  that  a  cubic  inch  of  gold  weighed  19 
ounces  out  of  water,  and  lost  one  ounce  of  its  weight 
by  being  weighed  in  water,  what  would  be  its  spe- 
citic  gravity  ? 

Caroline.  The  cubic  inch  of  water  it  displaced 
must  weigh  that  one  ounce ;  and  as  a  cubic  inch  of 
gold  weighs  19  ounces,  gold  is  19  times  as  heavy  ae 
water. 

Emily.  I  recollect  having  seen  a  table  of  the 
comparative  weights  of  bodies,  in  which  gold  appear- 
ed to  me  to  be  estimated  at  19  thousand  times  the 
weight  of  water. 

Mrs.  B.  You  misunderstood  the  meaning  of  the 
table.  In  the  estimation  you  allude  to,  the  weight  of 
water  was  reckoned  at  1000.  You  must  observe,  that 
the  weight  of  a  substance  when  not  compared  to  that 
of  any  other,  is  perfectly  arbitrary  ;  and  when  water 
is  adopted  as  a  standard,  we  may  denominate  its 
weight  by  any  number  we   please  ;    but  then   the 


156         MECHANICAL  PROPERTIES  OF  FLUIDS. 

weight  of  all  bodies  tried  by  this  standard  must  be 
signified  by  proportional  numbers. 

Caroline,  We  may  call  the  weii^ht  of  water,  for 
example,  one,  and  then  that  of  gold  would  be  nine- 
teen ;  or  if  we  chose  to  call  the  weight  of  water 
1000,  that  of  gold  would  be  19,000.  In  short,  the 
specific  gravity  means  how  much  more  a  body  weighs 
than  an  equal  bulk  <  f  water. 

Mrs.  B.  It  is  rather  the  weight  of  a  body  compa- 
red with  that  of  water  ;  for  the  specific  gravity  of 
many  substances  is  le»s  than  that  of  water. 

Caroline.  Then  you  cannot  ascertain  the  specific 
gravity  of  such  substances  in  the  same  manner  as  that 
of  gold  ;  for  a  body  that  is  lighter  than  water  will 
float  on  its  surface  without  displacing  any  water. 

Mrs.  B.  if  a  body  were  absolutely  light,  it  is  true 
that  it  would  not  displace  a  drop  of  water,  but  the  bo- 
dies we  are  treating  of  have  all  some  weight,  hovve- 
Ter  small ;  and  will,  therefore,  displace  some  quanti- 
ty of  water.  If  the  body  be  lighter  than  water,  it 
will  not  sink  to  a  level  with  the  surfiice  of  the  water, 
and  therefore  it  will  not  displace  so  much  water  as  is 
equal  to  its  bulk  ;  but  it  will  displace  as  much  as  is 
equal  to  its  weight.  A  ship,  you  must  have  observed, 
sinks  to  some  depth  in  water,  and  the  heavier  it  is  la- 
den the  deeper  it  sinks,  as  it  always  displaces  a  quan- 
tity of  water  equal  to  its  weight. 

Caroline.  But  you  said  just  now,  that  in  the  immer- 
sion of  gold,  the  bulk,  and  not  the  weight  of  body, 
was  to  be  considered.  , 

Mrs.  B.  That  is  the  case  with  all  substances 
which  are  heavier  than  water  ;  but  since  those  which 
are  lighter  do  not  displace  so  much  as  their  own  bulk^ 
the  quantity  they  displace  is  not  a  test  of  their  speci- 
fic gravity. 

In  order  to  obtain  the  specific  gravity  of  a  body 
which  is  lighter  than  water,  you  must  attach  to  it  a 
heavy  one,  whose  specific  gravity  is  known,  and  im- 
merse them  together  ;  the  specific  gravity  of  thp 
lighter  body  may  then  be  easily  calculated. 


MECHANICAL  PROPERTIES  OF  i  LUIJJa.         157 

Emily.  But  are  there  not  some  bodies  which  have 
Exactly  the  same  specific  gravity  as  water  ? 

Mrs.  B.  Undoubtedly  ;  and  such  bodies  will  re- 
main at  rest  in  whatever  situation  they  are  placed  in 
water.  Here  is  a  piece  of  wood  which,  by  being  im- 
pregnated with  a  little  sand,  is  rendered  precisely  of 
the  weight  of  an  equal  bulk  of  water;  in  whatever 
part  of  this  vessel  of  water  you  place  it,  you  will 
lind  that  it  will  remain  stationary. 

Caroline.  1  shall  first  put  it  at  the  bottom  ;  from 
thence,  of  course,  it  cannot  rise,  because  it  is  not 
lighter  than  water.  Now  I  shall  place  it  in  the  mid- 
dle of  the  vessel  ;  it  neither  rises  nor  sinks,  because 
it  is  neither  lighter  nor  heavier  than  the  water.  Now 
I  will  lay  it  on  the  surface  of  the  water ;  but  there  it 
sinks  a  little — what  is  the  reason  of  that,  Mrs.  B.  ? 

Mrs.  B.  Since  it  is  not  lighter  than  the  water,  it 
cannot  float  upon  its  surface  ;  since  it  is  not  heavier 
than  water,  it  cannot  sink  below  its  surface:  it  will 
sink,  therefore,  only  till  the  upper  surface  of  both  bo- 
dies are  on  a  level,  so  that  the  piece  of  wood  is  just 
covered  with  water.  If  you  poured  a  few  drops  of 
water  into  the  vessel,  (so  gently  as  not  to  increase 
their  momentum  by  giving  them  velocity,)  they  would 
mix  with  the  water  at  the  surface,  and  not  sink  lower. 

Caroline.  This  must,  no  doubt,  be  the  reason 
^vhy,  in  drawing  up  a  bucket  of  water  out  of  a  well, 
the  bucket  feels  so  much  heavier  when  it  rises  above 
the  surface  of  the  water  in  the  well«5  for  whilst  you 
raise  it  in  the  water,  the  water  within  the  bucket  be- 
ing of  the  same  specific  gravity  as  the  water  on  the 
outside,  will  be  wholly  supported  by  the  upward  pres- 
sure of  the  water  beneath  the  bucket,  and  conse- 
quently very  little  force  will  be  required  to  raise  it ; 
but  as  soon  as  the  bucket  rises  to  the  surface  of  the 
well,  you  immediately  perceive  the  increase  of 
weight. 

Emily.  And  how  do  you  ascertain  the  specific 
gravity  of  fluids  ? 

Mrs.  B.  By  means  of  an  instrument  called  a  hv- 
14 


158         MECHANICAL  PROPERTIES  OF  FLUIDS. 

drometer,  which  I  will  show  you.  It  consists  of  a 
thin  glass  ball,  A,  (fig.  8.  Plate  XIII.)  with  a  gradua- 
ted tube,  B,  and  the  specific  gravity  of  the  liquid  is  es- 
timated by  the  depth  to  which  the  instrument  sinks  in 
it.  There  is  a  smaller  ball,  C,  attached  to  the  in- 
strument below,  which  contains  a  little  mercury  ;  but 
this  is  merely  for  the  purpose  of  equipoising  the  in- 
strument, that  it  may  remain  upright  in  the  liquid  un- 
der trial. 

I  must  now  take  leave  of  you  ;  but  there  remain 
yet  many  observations  to  be  made  on  fluids  :  we 
shall,  therefore,  resume  this  subject  at  our  next  inter- 
view. 


CONVERSATION  XI. 


OF  SPRINGS,  FOUNTAINS,  &c. 

Of  the  Ascent  of  Vapour  mid  the  Formation  of  Clouds. 
~  Of  the  Formation  and  Fall  of  Rain,  <^c. — Of  the 
Formation  of  Springs. — Of  Rivers  and  Lakes. — Of 
Fountains. 

CAROLINE.  There  is  a  question  I  am  very  de- 
sirous of  asking  you  respecting  fluids,  Mrs.  B.,  which 
has  often  perplexed  me.  What  is  the  reason  that  the 
great  quantity  of  rain  which  falls  upon  the  earth  and 
sinks  into  it,  does  not,  in  the  course  of  time,  injure  its 
solidity  ?  The  sun  and  the  wind,  I  know,  dry  the  sur- 
face, but  they  have  no  effect  on  the  interior  parts, 
where  there  must  be  a  prodigious  accumulation  of 
moisture. 

Mrs.  B.  Do  you  not  know  that,  in  the  course  of 
time,  all  the  water  which  sinks  into  the  ground  rises 
out  of  it  again  ?  It  is  the  same  water  which  succes- 
sively forms  seas,  rivers,  springs,  clouds,  rain,  and 
sometimes  hail,  snow,  and  ice.  If  you  will  take  the 
trouble  of  following  it  through  these  various  changes, 
you  will  understand  why  the  earth  is  not  yet  drowned 
by  the  quantity  of  water  which  has  fallen  upon  it 
since  its  creation  ;  and  you  will  even  be  convinced, 
that  it  does  not  contain  a  single  drop  more  water 
now  than  it  did  at  that  period. 

Let  us  consider  how  the  clouds  were  originally 
formed.  When  the  first  rays  of  the  sun  warmed  the 
surface  of  the  earth,  the  heat,  by  separating  the  par- 
ticles of  water,  rendered  them  lighter  than  the  air. 


160  ON  SPRINGS,  FOUNTAINS,  &C. 

This,  you  know,  is  the  case  with  steam  or  vapour. 
What  then  ensues  ? 

Caroline.  When  lighter  than  the  air  it  will  natu- 
rally rise  ;  and  now  I  recollect  your  telling  us  in  a 
preceding  lesson,  that  the  heat  of  the  sun  transform- 
ed the  particles  of  water  into  vapour,  in  consequence 
of  which  it  ascended  into  the  atmosphere,  where  it 
formed  clouds. 

Mrs.  B.  We  have  then  already  followed  water 
through  two  of  its  transformations  :  from  water  it  her 
comes  vapour,  and  from  vapour  clouds. 

Emily.  But  since  this  watery  vapour  is  lighter 
than  the  air,  why  does  it  not  continue  to  rise  ;  and 
why  does  it  unite  again  to  form  clouds  ? 

Mrs.  B.  Because  the  atmosphere  diminishes  in 
density,  as  it  is  more  distant  from  the  earth.  The 
vapour,  therefore,  which  the  sun  causes  to  exhale, 
not  only  from  seas,  rivers,  and  lakes,  but  likewise 
from  the  moisture  on  the  land,  rises  till  it  reaches  a 
region  of  air  of  its  own  specific  gravity  ;  and  there, 
you  know,  it  will  remain  stationary.  By  the  fre- 
quent accession  of  fresh  vapour  it  gradually  accumu- 
lates, so  as  to  form  those  large  bodies  of  vapour, 
which  we  call  clouds  ;  and  these,  at  length,  becom- 
ing too  heavy  for  the  air  to  support,  they  fall  to  the 
ground. 

Caroline.  They  do  fall  to  the  ground,  certainly, 
when  it  rains  ;  but,  according  to  your  theory,  I  should 
have  imagined,  that  when  the  clouds  became  too  hea- 
vy for  the  region  of  air  in  which  they  were  situated 
to  support  them,  they  would  descend  till  they  reach- 
ed a  stratum  of  air  of  their  own  weight,  and  not  fall  to 
the  earth  ;  for  as  clouds  are  formed  of  vapour,  they 
cannot  be  so  heavy  as  the  lowest  regions  of  the  at- 
mosphere, otherwise  the  vapour  would  not  have  risen. 

Mrs.  B.  If  you  examine  the  manner  in  which  the 
clouds  descend,  it  will  obviate  tliis  objection.  In  fall- 
ing, several  of  the  watery  particles  come  within  the 
sphere  of  each  otlier's  attraction,  and  unite  in  the 
form  of  a  drop  of  water.     The  vapour,  thus  tran?- 


ON  SPRINGS,  F0CNTAINS,&C.  161 

formed  into  a  shower,  is  heavier  than  any  part  of  the 
atmosphere,  and  consequently  descends  to  the  earth. 

Caroline.     How  wonderfully  curious  I 

Mrs.  B.  It  is  impossible  to  consider  any  part  of 
nature  attentively  without  being  struck  with  admira- 
tion at  the  wisdom  it  displays  ;  and  I  hope  you  will 
never  contemplate  these  wonders  without  feeling 
your  heart  glow  with  admiration  and  gratitude  to- 
wards their  bounteous  Author.  Observe,  that  if  the 
waters  were  never  drawn  out  of  the  earth,  all  vege- 
tation would  be  destroyed  by  the  excess  of  moisture; 
if,  on  the  other  hand,  the  plants  were  not  nourished 
and  refreshed  by  occasional  showers,  the  drought 
would  be  equally  fatal  to  them.  If  the  clouds  con- 
stantly remained  in  a  state  of  vapour,  they  might,  as 
you  remarked,  descend  into  a  heavier  stratum  of  the 
atmosphere,  but  could  never  fall  to  the  ground  ;  or 
were  the  power  of  attraction  more  than  sufficient  to 
convert  the  vapour  into  drops,  it  would  transform  the 
cloud  into  a  mass  of  water,  which,  instead  of  nourish- 
ing, would  destroy  the  produce  of  the  earth. 

Water  then  ascends  in  the  form  of  vapour,  and 
descends  in  that  of  rain,  snow,  or  hail,  all  of  which 
ultimately  become  water.  Some  of  this  falls  into  the 
various  bodies  of  water  on  the  surface  of  the  globe, 
the  remainder  upon  the  land.  Of  the  latter,  part  re- 
ascends  in  the  form  of  vapour,  part  is  absorbed  by 
the  roots  of  vegetables,  and  part  descends  into  the 
bowels  of  the  earth,  where  it  forms  springs. 

Emily.     Is  rain  and  spring-water  then  the  same  ? 

Mrs.  B.  Yes,  originally.  The  only  difference 
between  rain  and  spring-water,  consists  in  the  foreign 
particles  which  the  latter  meets  with  and  dissolves  in 
its  passage  through  the  various  soils  it  traverses. 

Caroline.  Yet  spring  water  is  more  pleasant  to 
the  taste,  appears  more  transparent,  and,  I  should 
have  supposed,  would  have  been  more  pure  than  rain 
water. 

Mrs.  B.  No  ;  excepting  distilled  water,  rain  water 
is  the  most  pure  we  can  obtain  ;  and  it  is  its  purity 
14* 


16:2  ON  SPRINGS,  FOUNTAINS,  SzC, 

which  renders  it  insipid,  whilst  the  various  salts  and 
different  ingredients,  dissolved  in  spring  water,  give 
it  a  species  of  flavour,  without  in  any  degree  affecting 
Its  transparency  :  and  the  filtration  it  undergoes 
through  gravel  and  sand  in  the  bowels  of  the  earth, 
cleanses  it  from  all  foreign  matter  which  it  has  not 
the  power  of  dissolving. 

When  rain  falls  on  the  surface  of  the  earth,  it  con- 
tinues making  its  way  downwards  through  the  pores 
and  crevices  in  the  ground.  When  several  drops 
meet  in  their  subterraneous  passage,  they  unite  and 
form  a  little  rivulet  ;  this,  in  its  progress,  meets  with 
other  rivulets  of  a  similar  description,  and  they  pur- 
sue their  course  together  in  the  bowels  of  the  earth, 
till  they  are  stopped  by  some  substance  which  they 
cannot  penetrate. 

Caroline.  But  you  said  that  water  could  penetrate 
even  the  pores  of  gold,  and  they  cannot  meet  with  a 
substance  more  dense  ? 

Mrs.  B.  But  water  penetrates  the  pores  of  gold, 
only  when  under  a  strong  compressive  force,  as  in 
the  Florentine  experiment  ;  now,  in  its  passage  to- 
wards the  centre  of  the  earth,  it  is  acted  upon  by 
no  other  power  than  gravity,  which  is  not  sufficient  to 
make  it  force  its  way  even  through  a  stratum  of  clay. 
This  species  of  earth,  though  not  remarkably  dense, 
being  of  great  tenacity,  will  not  admit  the  particles 
of  water  to  pass.  When  water  encounters  any  sub- 
stance of  this  nature,  therefore,  its  progress  is  stopped, 
and  the  pressure  of  the  accumulating  waters  forms  a 
bed,  or  reservoir.  This  will  be  more  clearly  explained 
by  fig.  9.  Plate  XIII.  which  represents  a  section,  or 
the  interior  of  a  hill  or  mountain.  A,  is  a  body  of 
water  such  I  have  described,  which,  when  filled  up 
as  high  as  B,  (by  the  continual  accession  of  waters  it 
receives  from  the  ducts  or  rivulets  a,  a,  a,  a,)  finds  a 
passage  out  of  the  cavity,  and,  impelled  by  gravity,  it 
runs  on,  till  it  makes  its  way  out  of  the  ground  at  the 
fide  of  the  hill,  and  there  forms  a  spring,  C. 

Caroline,     Gravity  impels  downwards  towards  the 


©N  SPRINGS,  FOUNTAINS,  &LC,  16,3 

centre  of  the  earth  ;  and  the  spring  in  this  figure 
runs  in  a  horizontal  direction. 

Mrs.  B.  Not  entirely.  There  is  some  declivity 
from  the  reservoir  to  the  spot  where  the  water  issue* 
out  of  the  ground  :  and  gravity  you  know  will  bring 
bodies  down  an  inclined  plane,  as  well  as  in  a  per- 
pendicular direction. 

Caroline.  But  though  the  spring  may  descend,  on 
first  issuing,  it  must  afterwards  rise  to  reach  the  sur- 
face of  the  earth  ;  and  that  is  in  direct  opposition  to 
gravity. 

Mrs.  B.  A  spring  can  never  rise  above  the  level 
of  the  reservoir  whence  it  issues  ;  it  must,  therefore, 
find  a  passage  to  some  part  of  the  surface  of  the 
earth  that  is  lower  or  nearer  the  centre  than  the  re- 
servoir. It  is  true  that,  in  this  figure,  the  spring 
rises  in  its  passage  from  B  to  C  occasionally  ;  but 
this,  I  think,  with  a  little  reflection,  you  will  be  able 
to  account  for. 

Emily.  Oh,  yes ;  it  is  owing  to  the  pressure  of 
fluids  upwards,  and  the  water  rises  in  the  duct  upon 
the  same  principle  as  it  rises  in  the  spout  of  a  tea-pot ; 
that  is  to  say,  in  order  to  preserve  an  equilibrium 
with  the  water  in  the  reservoir.  Now  I  think  I  un- 
derstand the  nature  of  springs  :  the  water  will  flow 
through  a  duct,  whether  ascending  or  descending, 
provided  it  never  rises  higher  than  the  reservoir. 

Mrs.  B.  Water  may  thus  be  conveyed  to  every 
part  of  a  town,  and  to  the  upper  part  of  the  houses, 
if  it  is  originally  brought  from  a  height  superior  to 
any  to  which  it  is  conveyed.  Have  you  never  ob- 
iserved,  when  the  pavement  of  the  streets  has  beea 
mending,  the  pipes  which  serve  as  ducts  for  the  con- 
veyance of  the  water  through  the  town  ? 

Emily.  Yes,  frequently  ;  and  I  have  remarked 
that  when  any  of  these  pipes  have  been  opened,  the 
water  rushes  upwards  from  them  with  great  velocity, 
which,  I  suppose,  proceeds  from  the  pressure  of  the 
water  in  the  reservoir,  which  forces  it  out. 


164  ON  SPRINGS,  rOUNTAINS,  Lc. 

Caroline.  I  recollect  having  once  seen  a  very  cu- 
rious glass,  called  Tantalus's  cup  ;  it  consists  of  a 
goblet,  containing  a  small  figure  of  a  man,  and  whate- 
ver quantity  of  water  you  pour  into  the  goblet,  it  ne- 
ver rises  higher  than  the  breast  of  the  figure.  Do 
you  know  how  that  is  contrived  ? 

Mrs.  B.  It  is  by  means  of  a  syphon,  or  bent  tube, 
which  is  concealed  in  the  body  of  the  figure.  It  rises 
through  one  of  the  legs  as  high  as  the  breast,  and 
there  turning  descends  through  the  other  leg,  and 
from  thence  through  the  foot  of  the  goblet,  where  the 
water  runs  out.  (fig.  1.  Plate  XIV.)  When  you 
pour  water  into  the  glass  A,  it  must  rise  in  the  sy- 
phon B,  in  proportion  as  it  rises  in  the  glass  ;  and 
when  the  glass  is  filled  to  a  level  with  the  upper  part 
of  the  syphon,  the  water  will  run  out  through  the 
other  leg  of  the  figure,  and  will  continue  running  out, 
as  fast  as  you  pour  it  in  ;  therefore  the  glass  can  ne- 
ver fill  any  higher. 

Emify.  I  think  the  new  well  that  has  been  made 
at  our  country-house,  must  be  of  that  nature.  We 
had  a  great  scarcity  of  water,  and  my  father  has  been 
at  considerable  expense  to  dig  a  well  ;  after  penetrat- 
ing to  a  great  depth  before  water  could  be  found,  a 
spring  was  at  length  discovered,  but  the  water  rose 
only  a  few  feet  above  the  bottom  of  the  well ;  and 
sometimes  it  is  quite  dry. 

Mrs.  B.  This  has,  however,  no  analogy  to  Tanta- 
lus's cup,  but  is  owing  to  the  very  elevated  situation 
of  your  country-house. 

Emily.  I  believe  I  guess  the  reason.  There  can- 
not be  a  reservoir  of  water  near  the  summit  of  a  hill ; 
as  in  such  a  situation,  there  will  not  be  a  sufficient 
number  of  rivulets  formed  to  supply  one  ;  and  with- 
out a  reservoir  there  can  be  no  spring.  In  such  si- 
tuations, therefore,  it  is  necessary  to  dig  very  deep, 
in  order  to  meet  with  a  spring ;  and  when  we  give 
it  vent,  it  can  rise  only  as  high  as  the  reservoir  from 
whence  it  flows,  which  will  be  but  little,  as  the  reser- 


FLATE.  xnr. 


F^.   1. 


%•  ^• 


F^.  s 


ON  SPRINGS,  FOUNl'AINS,  &C.  166 

voir  must  be  situated  at  some  considerable  depth  be- 
low the  summit  of  the  hill. 

Caroline.  Your  explanation  appears  very  clear 
and  satisfactory  ;  but  1  can  contradict  it  from  experi- 
ence. At  the  very  top  of  a  hill,  near  our  country- 
house,  there  is  a  large  pond,  and,  according  to  your 
theory,  it  would  be  impossible  there  should  be  springs 
in  such  a  situation  to  supply  it  with  water.  Then 
you  know  that  1  have  crossed  the  Alps,  and  I  can  as- 
sure you,  that  there  is  a  fine  lake  on  the  summit  of 
Mount  Cenis,  the  highest  mountain  we  passed  over. 

Mrs.  B.  Were  there  a  lake  on  the  summit  of 
Mount  Blanc,  which  is  the  highest  of  the  Alps,  it 
would  indeed  be  wonderful.  But  that  on  Mount  Ce- 
nis is  not  at  all  contradictory  to  our  theory  of 
springs  ;  for  this  mountain  is  surrounded  by  others, 
much  more  elevated,  and  the  springs  which  feed  the 
lake  must  descend  from  reservoirs  of  water  formed  in 
those  mountains.  This  must  also  be  the  case  with  the 
pond  on  the  top  of  the  hill :  there  is  doubtless  some 
more  considerable  hill  in  the  neighbourhood,  which 
supplies  it  with  water. 

Emily.  1  comprehend  perfectly  why  the  water 
in  our  well  never  rises  high  ;  but  1  do  not  understand 
why  it  should  occasionally  be  dry. 

Mrs.  B.  Because  the  reservoir  from  which  it 
flows,  being  in  an  elevated  situation,  is  but  scantily 
supplied  with  water  ;  after  a  long  drought,  therefore, 
it  may  be  drained,  and  the  spring  dry,  till  the  reser- 
voir be  replenished  by  fresh  rains.  It  is  not  uncom- 
mon to  see  springs  flow  with  great  violence  in  wet 
weather,  and  at  other  times  be  perfectly  dry. 

Caroline.  But  there  is  a  spring  in  our  grounds 
»vhich  more  frequently  flows  in  dry  than  in  wet  wea- 
ther :  how  is  that  to  be  accounted  for  ? 

Mrs.  B.  The  spring  probably  comes  from  a 
reservoir  at  a  great  distance,  and  situated  very  deep 
in  the  ground  ;  it  is,  therefore,  some  length  of  time 
before  the  rain  reaches  the  reservoir,  and  another 
considerable  portion  must  elapse,  whilst  the  water  is 


166  ON  SPRINGS,  FOUNTAINS,  &€. 

making  its  way  from  the  reservoir  to  the  surface  of 
the  earth  ;  so  that  the  dry  weather  may  probably 
have  succeeded  the  rains  before  the  spring  begins  to 
flow,  and  the  reservoir  may  be  exhausted  by  the  time 
the  wet  weather  sets  in  again. 

Caroline.  I  doubt  not  but  this  is  the  case,  as  the 
spring  is  in  a  very  levy  situation,  therefore  the  reser- 
voir may  be  at  a  great  distance  from  it. 

Mrs.  B.  Springs  which  do  not  constantly  flow,  are 
called  intermitting,  and  are  occasioned  by  the  reser- 
voir being  imperfectly  supplied.  Independently  of 
the  situation,  this  i^  always  the  case  when  the  duct  or 
ducts  which  convey  the  water  into  the  reservoir  are 
smaller  than  those  which  carry  it  off". 

Caroline.  If  it  runs  out  faster  than  it  runs  in,  it  will 
of  course  sometimes  be  empty.  And  do  not  rivers  al- 
so derive  their  source  from  springs  ? 

Mrs.  B.  Yes,  they  generally  take  their  source  in 
mountainous  countries,  where  springs  are  most  abun- 
dant. 

Caroline.  I  understood  you  that  springs  were 
more  rare  in  elevated  situations. 

Mrs.  B.  You  do  not  consider  that  mountainous 
countries  abound  equally  with  high  and  low  situa- 
tions. Reservoirs  of  water,  which  are  formed  in  the 
bosom  of  mountains,  generally  find  a  vent  either  on 
their  declivity,  or  in  the  valley  beneath  ;  while  sub- 
terraneous reservoirs,  formed  in  a  plain,  can  seldom 
find  a  passage  to  the  surface  of  the  earth,  but  remain 
concealed,  unless  discovered  by  digging  a  well. 
When  a  spring  once  issues  at  the  surface  of  the  earth 
it  continues  its  course  externally,  seeking  always  a 
lower  ground,  for  it  can  no  longer  rise. 

Emily.  Then  what  is  the  consequence,  if  the 
spring,  or  I  should  now  rather  call  it  a  rivulet,  runs 
into  a  situation  which  is  surrounded  by  higher 
ground. 

Mrs.  B.  Its  course  is  stopped,  the  water  accumu- 
lates, and  it  forms  a  pool,  pond,  or  lake,  according  to 
the  dimensions  of  the  body  of  water.     The  Lake  of 


6N  SPRINGS,  FOUNTAINS,  &e»  165' 

Geneva,  in  all  probability,  owes  its  origin  to  the 
Rhone,  which  passes  through  it :  if,  when  this  river 
first  entered  the  valley,  which  now  forms  the  bed  of 
the  Lake,  it  found  itself  surrounded  by  higher 
grounds,  its  waters  would  there  accumulate,  till  they 
rose  to  a  level  with  that  part  of  the  valley  where  the 
Rhone  now  continues  its  course  beyond  the  Lake,  and 
from  whence  it  flows  through  valleys,  occasionally 
forming  other  small  lakes,  till  it  reaches  the  sea. 

Emily.  And  are  not  fountains  of  the  nature  of 
springs  ? 

Airs.  B.  Exactly.  A  fountain  is  conducted  per- 
pendicularly upwards,  by  the  spout  or  adjutage  A, 
through  which  it  flows  ;  and  it  will  rise  nearly  as 
high  as  the  reservoir  B,  from  whence  it  proceeds, 
(Plate  XIV.  tig.  2.) 

Caroline.     Why  not  quite  as  high  ? 

Mrs.  B.  Because  it  meets  with  resistance  from 
the  air  in  its  ascent  ;  and  its  motion  is  impeded  by 
friction  against  the  spout,  where  it  rushes  out. 

Emily.  But  if  the  t«ibe  through  which  the  water 
rises  be  smooth,  can  there  be  any  friction  ?  especial- 
ly with  a  fluid,  whose  particles  yield  to  the  slightest 
impression. 

Airs.  B.  Friction  (as  we  observed  in  a  former 
lesson)  may  be  diminished  by  polishing,  but  can  ne- 
ver be  entirely  destroyed  ;  and  though  fluids  are  less 
susceptible  of  friction  than  solid  bodies,  they  are  still 
afiected  by  it.  Another  reason  why  a  fountain  will 
not  rise  so  high  as  its  reservoir,  is,  that  as  all  the  par- 
ticles of  water  spout  from  the  tube  with  an  equal  ve- 
locity, and  as  the  pressure  of  the  air  upon  the  exte- 
rior particles  must  diminish  their  velocity,  they  will 
in  some  degree  strike  against  the  under  parts,  and 
force  them  sideways,  spreading  the  column  into  a 
head,  and  rendering  it  both  wider  and  shorter  than  it 
otherwise  would  be. 

At  our  next  meeting,  we  shall  examine  the  mecha- 
nir'al  properties  of  the  air,  which,  being  an  elastic 
fluid,  differs  in  many  respects  from  liquids. 


CONVERSATION  XH. 


ON  THE  MECHANICAL  PROPERTIES  OF  AIR. 

Of  the  Spring  or  Elasticity  of  the  Air. — Of  the  "weight 
of  the  Air. — Experiments  with  the  Air  Pump. — Of 
the  Barometer. — Mode  of  weighing  Air. — Specific 
Gravity  of  Air. — Of  Pumps. — Description  of  the 
Sucking  Pump. — Description  of  the  Forcing  Pump. 

MRS.  B.  At  our  last  meeting  we  examined  the 
properties  of  fluids  in  fijeneral,  and  more  particularly 
of  such  fluids  as  are  called  liquids. 

There  is  another  class  of  fluids,  distinguished  by 
the  name  of  aeriform  or  elastic  fluids,  the  principal 
of  which  is  the  air  we  breathe,  which  surrounds  the 
earth,  and  is  called  the  atmosphere. 

Emily.  There  are  then  other  kinds  of  air  besides 
the  atmosphere  ? 

Mrs.  B.  Yes,  a  great  variety  ;  but  they  differ  only 
in  their  chemical,  and  not  in  their  mechanical  pro- 
perties ;  and  as  it  is  the  latter  we  are  to  examine,  we 
shall  not  at  present  inquire  into  their  composition,  but 
confme  our  attention  to  the  mechanical  properties  of 
elastic  fluids  in  general. 

Caroline.    And  from  whence  arises  this  difference  ? 

Mrs.  B.  There  is  no  attraction  of  cohesion  be- 
tween the  particles  of  elastic  fluids  ;  so  that  the  ex- 
pansive power  of  heat  has  no  adversary  to  contend 
with  but  gravity  ;  any  increase  of  temperature,  there- 
fore, expands  elastic  fluids  prodigiously,  and  a  dimi- 
nution proportionally  condenses  them. 


MECHANICAL   PROPERTIES  OP  AIR.  16!^ 

The  most  essential  point  in  which  air  differs  from 
other  fluids,  is  .by  its  spring  or  elasticity  ;  that  is  to 
say,  its  power  of  increasing  or  diminishing  in  bulk, 
according  as  it  i?  more  or  less  compressed  :  a  power 
of  which  I  have  mformed  you  liquids  are  almost 
wholly  deprived. 

Emily.  I  think  I  understand  the  elasticity  of  the 
air  very  well,  from  what  you  formerly  said  of  it  ;* 
but  wluit  perplexes  me  is,  its  having  gravity  ;  if  it  is 
heavy,  and  we  are  surrounded  by  it,  why  do  we  not 
feel  its  weight  ? 

Caroline.  It  must  be  impossible  to  be  sensible  of 
the  weight  of  such  infinitely  small  particles,  as  those 
of  which  the  air  is  composed  :  particles  which  are 
too  small  to  be  seen,  must  be  too  light  to  be  felt. 

Mrs.  B.  You  are  mistaken,  my  dear  ;  the  air  is 
much  heavier  than  you  imagine  ;  it  is  true,  that  the 
particles  which  compose  it  are  small  ;  but  then,  re- 
flect on  their  quantity  :  the  atmosphere  extends  to 
about  the  distance  of  45  miles  from  the  earth,  and  its 
gravity  is  such,  that  a  man  of  middling  stature  is  com- 
puted (when  the  air  is  heaviest)  to  sustain  the  weight 
of  about  14  tons. 

Caroline.  Is  it  possible  !  I  should  have  thought 
such  a  weight  would  have  crushed  any  one  to  atoms. 

Mrs.  B.  That  would,  indeed,  be  the  case,  if  it 
were  not  for  the  equality  of  the  pressure  on  every 
part  of  the  body;  but,  when  thus  diffused,  we  can 
bear  even  a  much  greater  weight,  without  any  consi- 
derable inconvenience.  In  bathing  we  support  the 
weight  and  pressure  of  the  water,  in  addition  to  that 
of  the  atmosphere  ;  but  because  this  pressure  is 
equally  distributed  over  the  body,  we  are  scarcely 
sensible  of  it  ;  whilst  if  your  shoulders,  your  head, 
or  any  particular  part  of  your  frame  were  loaded 
with  the  additional  weight  of  a  hundred  pounds,  you 
■would  soon  sink  under  the  fatigue.     Besides  this,  our 


See  page  37- 


170  MECHANICAL  PROPERTIEa  OP  AIR. 

bodies  contain  air,  the  spring  of  which  counterbalan- 
ces the  weight  of  the  external  air,  and  renders  us  less 
sensible  of  its  pressure. 

Caroline.  But  if  it  were  possible  to  relieve  me 
from  the  weight  of  the  atmosphere,  should  I  not  feel 
more  light  and  agile  ? 

Mrs.  B.  On  the  contrary,  the  air  within  you 
meeting  with  no  external  pressure  to  restrain  its  elas- 
ticity, would  distend  your  body,  and  at  length,  burst- 
ing the  parts  which  confined  it,  put  a  period  to  your 
existence. 

Caroline.  This  weight  of  the  atmosphere,  then, 
which  I  was  so  apprehensive  would  crush  me,  is,  in 
reality,  essential  to  my  preservation. 

Emily.  J  once  saw  a  person  cupped,  and  was  told 
that  the  swelling  of  the  part  under  the  cup  was  produ- 
ced by  taking  away  from  that  part  the  pressure  of  the 
atmosphere  ;  but  1  could  not  understand  how  this 
pressure  produced  such  an  effect. 

JUrs.  B.  The  air  pump  affords  us  the  means  of 
making  a  great  variety  of  interesting  experiments  on 
the  weight  and  pressure  of  the  air  :  some  of  them 
you  have  already  seen.  Do  you  not  recollect,  that  in 
a  vacuum  produced  within  the  air-pump,  substances 
of  various  weights  fell  to  the  bottom  in  the  same 
time  ;  why  does  not  this  happen  in  tlie  atmosphere  ? 

Caroline.  I  remember  you  told  us  it  was  owing  to 
the  resistance  which  light  bodies  meet  with  from  the 
air  during  their  fall. 

Mrs.  B.  Or,  in  other  words,  to  the  support  which 
they  received  from  the  air,  and  which  prolonged  the 
time  of  their  fall.  Now,  if  the  air  were  destitute  of 
weight,  how  could  it  support  other  bodies,  or  retard 
their  fall  ? 

I  shall  now  show  you  some  other  experiments, 
which  illustrate,  in  a  striking  manner,  both  the 
weight  and  elasticity  of  air.  1  shall  tie  a  piece  of 
bladder  over  this  glass  receiver,  which,  you  will  ob- 
serve, is  open  both  at  the  top  as  well  as  below. 

Caroline,     Why  do  you  wet  the  bladder  first  ? 


MECHANICAL  PROPERTIES  OF  AIR.  171 

Mrs,  B.  It  expands  by  wetting,  and  contracts  in 
drying  ;  it  is  also  more  soft  and  pliable  when  wet,  so 
that  I  can  make  it  tit  better,  and  when  dry  it  will  be 
tighter.  We  must  hold  it  to  the  fire  in  order  to  dry  ; 
but  not  too  near,  least  it  should  burst  by  sudden  con- 
traction. Let  us  now  fix  it  on  the  air-pump  and  ex- 
haust the  air  from  underneath  it — you  will  not  be 
alarmed  if  you  hear  a  noise  ? 

Eniihf.  It  was  as  loud  as  the  report  of  a  gun,  and 
the  bladder  is  burst !  Pray  explain  how  the  air  is  con- 
cerned in  this  experiment. 

Mrs.  B.  It  is  the  effect  of  the  weight  of  the  at- 
mosphere on  the  upper  surface  of  the  bladder,  when 
I  had  taken  away  the  air  from  the  under  surface  ;  so 
that  there  was  no  longer  any  reaction  to  counterba- 
lance the  pressure  of  the  atmosphere  on  the  receiver. 
You  observed  how  the  bladder  was  pressed  inwards 
by  Ihe  weight  of  the  external  air,  in  proportion  as  I 
exhausted  the  receiver  :  and  before  a  complete  va- 
cuum was  formed,  the  bladder,  unable  to  sustain  the 
violence  of  the  pressure,  burst  with  the  explosion 
you  have  just  heard. 

I  shall  now  show  you  an  experiment,  which  proves 
the  expansion  of  the  air,  contained  within  a  body 
when  it  is  relieved  from  the  pressure  of  the  external 
air.  You  would  not  imagine  that  there  was  any  air 
contained  within  this  shrivelled  apple,  by  its  appear- 
ance ;  but  take  notice  of  it  when  placed  within  a  re- 
ceiver, from  which  1  shall  exhaust  the  air. 

Caroline.  How  strange !  it  grows  quite  plump, 
and  looks  like  a  fresh-gathered  apple. 

Mrs.  B.  But  as  soon  as  I  let  the  air  again  into  the 
receiver,  the  apple  you  see  returns  to  its  shrivelled 
state.  When  1  took  away  the  pressure  of  the  atmos- 
phere, the  air  within  the  apple  expanded  and  swell- 
ed it  out ;  but  the  instant  the  atmospherical  air  was 
restored,  the  expansion  of  the  internal  air  was  check- 
ed and  repressed,  and  the  apple  shrunk  to  its  former 
dimensions. 

You  may  make  a  similar  experiment  with  this  lit- 


172  MECHANICAL  PROPERTIL     OF  AIR. 

tie  bladder,  which  you  see  is  perfectly  flaccid,  an^ 
appears  to  contain  no  air  :  in  this  state,  i  shall  tie  up 
the  neck  of  the  bladder,  so  that  whatever  air  remains 
within  it  may  not  escape,  and  then  place  it  under  the 
receiver.  Now  observe,  as  I  exhaust  the  receiver, 
iiow  the  bladder  distends  ;  this  proceeds  from  the 
great  dilatation  of  the  small  quantity  of  air  which  was 
enclosed  within  the  bladder  when  1  tied  it  up  ;  but  as 
soon  as  I  let  the  air  into  the  receiver,  that  which  the 
hladder  contains  condenses,  and  shrinks  into  its  small 
©ompass  within  the  folds  of  the  bladder. 

Emily.  These  experiments  are  extremely  amU' 
sing,  and  they  afl'ord  clear  proofs  both  of  the  weight 
and  elasticity  of  the  air;  but  I  should  like  to  know 
exactly  how  much  the  air  weighs. 

Mrs.  B.  A  column  of  air  reaching  to  the  top  of  the 
atmosphere,  and  whose  base  is  a  square  inch,  wej^hs 
15  lbs.  when  the  air  is  heaviest;  therefore  every 
square  inch  of  our  bodies  sustains  a  weight  of  15  lbs.  : 
and  if  you  wish  to  know  the  weight  of  the  whole  of 
the  atmosphere,  you  must  reckon  how  many  square 
inches  there  are  on  the  surface  of  the  globe,  and 
multiply  them  by  15. 

Emily.     But  are   there  no  means  of  ascertaining, 
the  weight  of  a  small  quantity  of  air  1 

Mrs.  B.  Nothing  more  easy.  I  shall  exhaust  the 
air  from  this  little  bottle  by  means  of  the  air-pump  ; 
and  having  emptied  the  bottle  of  air,  or,  in  other 
words,  produced  a  vacuum  within  it,  I  secure  it  by- 
turning  this  screw  adapted  to  its  neck  :  we  may  now 
find  the  exact  weight  of  this  bottle,  by  putting  it  into 
one  of  the  scales  of  a  balance.  Jt  weighs  you  see 
just  two  ounces  ;  but  when  1  turn  the  screw,  so  as  to 
admit  the  air  into  the  bottle,  the  scale  which  contains 
it  preponderates. 

Caroline.  No  doubt  the  bottle  filled  with  air  is 
heavier  than  the  bottle  void  of  air  ;  and  the  addition- 
al weight  required  to  bring  the  scales  again  to  a  ba- 
lance, must  be  exactly  that  of  the  air  which  the  bot- 
tle now  contains^ 


MECHANICAL  PROPERTIES  OF  AIR.  173 

Mrs.  B.  That  weight,  you  see,  is  almost  two 
grains.  The  dimensions  of  this  bottle  are  six  cubic 
inches.  Six  cubic  inches  of  air,  therefore,  at  the 
temperature  of  this  room,  weighs  nearly  2  grains. 

Caroline.  Why  do  you  observe  the  temperature 
of  the  room,  in  estimating  the  weight  of  the  air. 

Mrs.  B.  Because  heat  rarefies  air,  and  renders  it 
lighter  ;  therefore  the  warmer  the  air  is  which  you 
weigh,  the  lighter  it  will  be. 

If  you  should  now  be  desirous  of  knowing  the  spe- 
cific gravity  of  this  air,  we  need  only  fill  the  same 
bottle  with  water,  and  thus  obtain  the  weight  of  an 
equal  quantity  of  water — which  you  see  is  1515  grs.  j 
now  by  comparing  the  weight  of  water  to  that  of  air, 
we  find  it  to  be  in  the  proportion  of  about  800  to  1. 

1  will  show  you  another  instance  of  the  weight  of 
the  atmosphere,  which  I  think  will  please  you  :  you 
know  what  a  barometer  is  ? 

Caroline.  It  is  an  instrument  which  indicates  the 
state  of  the  weather,  by  means  of  a  tube  of  quicksil- 
ver ;   but  how,  I  cannot  exactly  say. 

Mrs.  B.  It  is  by  showing  the  weight  of  the  atmos- 
phere. The  barometer  is  an  instrument  extremely 
simple  in  its  construction :  in  order  that  you  may  un- 
derstand it,  I  will  show  you  how  it  is  made  I  first 
fill  a  glass  tube  A  B,  (fig.  3.  Plate  XIV.)  about  three 
feet  in  length,  and  open  only  at  one  end,  with  mercu- 
ry ;  then  stopping  the  open  end  with  my  finger,  I  im- 
merse it  in  a  cup  C,  containing  a  little  mercury. 

Emily.  Part  of  the  mercury  which  was  in  the 
tube,  I  observe,  runs  down  into  the  cup  ;  but  why 
does  not  the  whole  of  it  subside  in  the  cup,  for  it  is 
contrary  to  the  law  of  the  equilibrium  of  fluids,  that 
the  mercury  in  the  tube  should  not  descend  to  a  level 
with  that  in  the  cup  ? 

Mrs.  B.  The  mercury  that  has  fallen  from  the 
tube  into  the  cup,  has  left  a  vacant  space  in  the  up- 
per part  of  the  tube,  to  which  the  air  cannot  a,ain  ac- 
cess ;  this  space  is  therefore  a  perfect  vacuum  ;  and 
consequently  the  mercury  in  the  tube  is  relieved 
15* 


174  MECHANICAL  PROPERTIES  OF  AIK. 

from  the  pressure  of  the  atmosphere,  whilst  that  m 
the  cup  remains  exposed  to  it. 

Caroline.  Oh,  now  I  understand  it ;  the  pressure 
of  the  air  on  the  mercury  in  the  cup  forces  it  to  rise 
in  the  tube,  where  it  sustains  no  pressure. 

Emily.  Or  rather  supports  the  mercury  in  the 
tube,  and  prevents  it  from  faUing. 

Mrs.  B.  That  comes  to  the  same  thing  ;  for  the 
power  that  can  support  mercury  in  a  vacuum,  would 
also  make  it  ascend  when  it  met  with  a  vacuum. 

Thus  you  see,  that  the  equilibrium  of  the  mercu- 
ry is  destroyed  only  to  preserve  the  general  equili- 
brium of  fluids. 

Caroline.  But  this  simple  apparatus  is,  in  appear- 
ance, very  unlike  a  barometer. 

Mrs.  B.  It  is  all  that  is  essential  to  a  barometer. 
The  tube  and  the  cup  or  vase  are  fixed  on  a  board, 
for  the  convenience  of  suspending  it ;  the  board  is 
graduated  for  the  purpose  of  ascertaining  the  height 
at  which  the  mercury  stands  in  the  tube  ;  and  the 
small  moveable  metal  plate  serves  to  show  that 
height  with  greater  accuracy. 

Emilij.  And  at  what  height  will  the  weight  of  the 
atmosphere  sustain  the  mercury  ? 

Mrs.  B.  About  28  inches,  as  you  will  see  by  this 
barometer  ;  but  it  depends  upon  the  weight  of  the 
atmosphere,  which  varies  much  according  to  the  state 
of  the  weather.  The  greater  the  pressure  of  the 
air  on  the  mercury  in  the  cup,  the  higher  it  will  as-^ 
cend  in  the  tube.  Now  can  yon  tell  me  whether  the 
air  is  heavier  in  wet  or  dry  weather. 

Caroline.  Without  a  moment's  reflection,  the  air 
roust  be  heaviest  in  wet  weather.  It  is  so  depress- 
ing, and  makes  one  feel  so  heavy  ;  while  in  fine 
weather  I  feel  as  light  as  a  feather,  and  as  brisk  as 
a  bee. 

Mrs.  B.  Would  it  not  have  been  better  to  have 
answered  with  a  moment's  reflection,  Caroline  ?  It 
wonld  have  convinced  you,  that  the  air  must  be  hea^ 
yrest  in  dry  weather,  for  it  is  then  that  the  mercurv 


MECHANICAL  1»R0PERTIES  OP  AIR.  17a 

i3  tbund  to  rise  in  the  tube,  and  consequently  the 
mercury  in  the  cup  must  be  most  pressed  by  the  air  : 
and  yow  know,  that  we  estimate  tlie  dryness  and  fair- 
ness of  the  weather  by  the  height  of  the  mercury  in 
the  barometer. 

Caroline.  Why  then  does  the  air  feel  so  heavy  in 
bad  weather. 

Mrs.  B.  Because  it  is  less  salubrious  when  im- 
pregnated with  damp.  The  lungs  under  these  cir- 
cumstances do  not  play  so  freely,  nor  does  the  blood 
circulate  so  well :  thus  obstructions  are  frequently 
occasioned  in  the  smaller  vessels,  from  which  arise 
colds,  asthmas,  agues,  fevers,  &:c. 

Emily.  Since  the  atmosphere  diminishes  in  densi- 
ty in  the  upper  regions,  is  not  the  air  more  rare  upon 
a  hill  than  in  a  plain  ;  and  does  the  barometer  indi- 
cate this  difference  ? 

Mrs.  B.  Certainly.  The  hills  in  this  country  are 
not  sufficiently  elevated  to  produce  any  very  conside- 
rable effect  on  the  barometer  ;  but  this  instrument  is 
so  exact  in  its  indications,  that  it  is  used  for  the  pur- 
pose of  measuring  the  height  of  mountains,  and  of  es- 
timating the  elevation  of  balloons. 

Emily.  And  is  no  inconvenience  experienced  from 
the  thinness   of  the   air  in  such  elevated  situations  ? 

Mrs.  B.  Oh,  yes  ;  frequently.  It  is  sometimes 
oppressive,  from  being  insufficient  for  respiration  ; 
and  the  expansion  which  takes  place  in  the  more 
dense  air  contained  within  the  body  is  often  painful  ; 
it  occasions  distension,  and  sometimes  causes  the 
bursting  of  the  smaller  blood-vessels  in  the  nose  and 
ears.  Besides,  in  such  situations,  you  are  more  ex- 
posed both  to  heat  and  cold  ;  for  though  the  atmos- 
phere is  itself  transparent,  its  lower  regions  abound 
with  vapours  and  exhalations  from  the  earth,  which 
float  in  it,  and  act  in  some  degree  as  a  covering, 
which  preserves  us  equally  from  the  intensity  of  the 
sun's  rays,  and  from  the  severity  of  the  cold. 

Caroline.  Pray,  Mrs.  B.,  is  not  the  thermometer 
(Jonstrqcted  on  the  same  principles  as  the  barometer  ? 


176  MECHANICAL  PROPERTIES  OF  AIR. 

Mrs.  B.  Not  at  all.  The  rise  and  fall  of  the  fluid 
in  the  thermometer  is  occasioned  by  the  expansive 
power  of  heat,  and  the  condensation  produced  by 
cold  :  the  air  has  no  access  to  it.  An  explanation  of 
it  would,  therefore,  be  irrelevant  to  our  present  sub- 
ject. 

Emily.  I  have  been  reflecting,  that  since  it  is  the 
weight  of  the  atmosphere  which  supports  the  mercu- 
ry in  the  tube  of  a  barometer,  it  would  support  a  co- 
lumn of  any  other  fluid  in  the  same  manner. 

Mrs.  B.  Certainly  ;  but  as  mercury  is  heavier 
than  all  other  fluids,  it  will  support  a  higher  column 
of  any  other  fluid  ;  for  two  fluids  are  in  equilibrium, 
*vhen  their  height  varies  inversely  as  their  densities. 
We  find  the  weight  of  the  atmosphere  is  equal  to  sus- 
taining a  column  of  water,  for  instance,  of  no  less  than 
32  feet  above  its  level. 

Caroline.  The  weight  of  the  atmosphere  is,  then, 
as  great  as  that  of  a  body  of  water  the  depth  of  32  feet  ? 

Mrs.  B.  Precisely  ;  for  a  column  of  air  of  the 
height  of  the  atmosphere  is  equal  to  a  column  of  wa- 
ter of  32  feet,  or  one  of  mercury  of  28  inches. 

The  common  pump  is  constructed  on  this  princi- 
ple. By  the  act  of  pumping,  the  pressure  of  the  at- 
mosphere is  taken  off"  the  water,  which,  in  conse- 
quence, rises. 

The  body  of  a  pump  consists  of  a  large  tube  or 
pipe,  whose  lower  end  is  immersed  in  the  water 
which  it  is  designed  to  raise.  A  kind  of  stopper,  call- 
ed a  piston,  is  fitted  to  this  tube,  and  is  made  to  slide 
up  and  down  it,  by  means  of  a  metallic  rod  fastened  t© 
the  centre  of  the  piston. 

Emily.  Is  it  not  similar  to  the  syringe,  or  squirt, 
with  which  you  first  draw  in,  and  then  force  out  wa- 
ter ? 

Mrs.  B.  It  is  ;  but  you  know  that  we  do  not  wish 
to  force  the  water  out  of  the  pump,  at  the  same  end 
of  the  pipe  at  which  we  draw  it  in.  The  intention  of 
a  pump  is  to  raise  water  from  a  spring  or  well ;  the 


MECHANICAL  PROPERTIES  OP  AIR.  177 

pipe  is,  therefore,  placed  perpendicularly  over  the 
water,  which  enters  it  at  the  lower  extremity,  and  it 
issues  at  a  horizontal  spout  towards  the  upper  part  of 
the  pump.  The  pump,  therefore,  is  rather  a  more 
complicated  piece  of  machinery  than  the  syringe. 
^  Its  various  parts  are  delineated  in  this  tigure  : 
(fi^.  4.  Plate  XIV.)  A  B  is  the  pipe  or  hody  of  the 
pump,  P  the  piston,  V  a  valve,  or  little  door  in  the 
piston,  which,  opening  upwards,  admits  the  water  to 
rise  through  it,  but  prevents  its  returning,  and  Y  a 
similar  valve  in  the  body  of  the  pump. 

When  the  pump  is  in  a  state  of  inaction,  the  two 
valves  are  closed  by  their  own  weight ;  but  when, 
by  drawing  down  the  handle  of  the  pump,  the  piston 
ascends,  it  raises  a  column  of  air  which  rested  upon  it, 
and  produces  a  vacuum  between  the  piston  and  the 
lower  valve  Y,  the  air  beneath  this  valve,  which  is 
immediately  over  the  surface  of  the  water,  conse- 
quently expands,  and  forces  its  way  through  it ;  the 
water,  then,  relieved  from  the  pressure  of  the  air,  as- 
cends into  the  pump.  A  few  strokes  of  the  handle 
totally  excludes  the  air  from  the  body  of  the  pump» 
and  fills  it  with  water,  which,  having  passed  through 
both  the  valves,  runs  out  at  the  spout. 

Caroline.  I  understand  this  perfectly.  When  the 
piston  is  elevated,  the  air  and  the  water  successively 
rise  in  the  pump  ;  for  the  same  reason  as  the  mercu- 
ry rises  in  the  barometer. 

Emily.  I  thought  that  water  was  drawn  up  into  a 
pump,  by  suction,  in  the  same  manner  as  water  may 
be  sucked  through  a  straw. 

Airs.  B.  It  is  so,  into  the  body  of  the  pump  ;  for 
the  power  of  suction  is  no  other  than  that  of  produ- 
cing a  vacuum  over  one  part  of  the  liquid,  into  which 
vacuum  the  liquid  is  forced  by  the  pressure  of  the  at-  "^ 
mosphere  on  another  part.  The  action  of  sucking 
througli  a  straw  consists  in  drawing  in  and  conhning^ 
the  breath,  so  as  to  produce  a  vacuum  in  the  mouth  ; 
in  consequence  of  which,  the  air  within  the  straw 
rushes  into  the  mouth,  and  is  followed  by  the.  liquid. 


178  MECHANICAL  PROPERTIES  OF  AIR. 

into  which  the  lower  end  of  the  straw  is  immersed. 
The  principle,  you  see,  is  the  same  ;  and  the  only 
difference  consists  in  the  mode  of  producing  a  vacuum. 
In  suction,  the  muscular  powers  answer  the  purpose 
of  the  piston  and  valves. 

Emily.  Water  cannot,  then,  be  raised  by  a  pump 
above  32  feet;  for  the  pressure  of  the  atmosphere 
will  not  sustain  a  column  of  water  above  that  height. 

Mrs.  B.  1  beg  your  pardon.  It  is  true  that  there 
must  never  be  so  ii;reat  a  distance  as  32  feet  from  the 
level  of  the  water  in  the  well,  to  the  valve  in  the  pis- 
ton, otherwise  the  water  would  not  rise  through  that 
valve  ;  but  when  once  the  water  has  passed  that  open- 
ing, it  is  no  longer  the  pressure  of  air  on  the  reservoir 
which  makes  it  ascend  ;  it  is  raised  by  lifting  it  up,  as 
you  would  raise  it  in  a  bucket,  of  which  the  piston 
formed  the  bottom.  This  common  pump  is,  there- 
fore, called  the  sucking,  or  lifting-pump,  as  it  is  con- 
structed on  both  these  principles.  There  is  another 
sort  of  pump,  called  the  forcing-pump  :  it  consists  of 
a  forcing  power  added  to  the  sucking  part  of  the  pump. 
This  additional  power  is  exactly  on  the  principle  of 
the  syringe  :  by  raising  the  piston  you  draw  the  water 
into  the  pump,  and  by  descending  it  you  force  the  wa- 
ter out. 

Caroline.  But  the  water  must  be  forced  out  at  the 
upper  part  of  the  pump  ;  and  I  cannot  conceive  how 
that  can  be  done  by  descending  the  piston. 

Mrs.  B.  Figure  6.  PI.  XIV.  will  explain  the  diffi- 
culty. The  large  pipe  A  B  represents  the  sucking 
part  of  the  pump,  which  differs  from  the  lifting-pump 
only  in  its  piston  P  being  unfurnished  with  a  valve,  in 
consequence  of  which  the  water  cannot  rise  above  it. 
When,  therefore,  the  piston  descends,  it  shuts  the 
valve  Y,  and  forces  the  water  (which  has  no  other 
vent)  into  the  pipe  D  :  this  is  likewise  furnished  with 
a  valve  V,  which,  opening  outwards,  admits  the  wa- 
ter, but  prevents  its  return. 

The  water  is  thus  first  raised  in  the  pump,  and  then 
forced  into  the  pipe,  by  the  alternate  ascending  and 


MECHANICAL  PROPERTIES  OF  AIR,  179 

descendini;  motion  of  the  piston,  after  a  few  strokes 
of  the  handle  to  till  the  pipe,  from  whence  the  water 
i.-       s  at  the  spout. 

h  is  now  time  to  conclude  our  lesson.  When 
next  we  meet,  1  shall  give  you  some  account  of  wind, 
and  of  sound,  which  will  terminate  our  observations 
on  elastic  fluids. 

Caroline.  And  I  shall  run  into  the  garden,  to  have 
the  pleasure  of  pumping,  now  that  1  understand  the 
construction  of  a  pump. 

Mrs.  B.  And,  to-morrow,  I  hope  you  will  be  able 
to  tell  me,  whether  it  is  a  forcing  or  a  common  lifting 
pump. 


CONVERSATION  XIII. 


ON  WIND  AND  SOUND. 

Of  Wind  in  General.— Of  the  Trade  Wind.— Of  the 
Perwdical  Trade  Winds. — Of  the  Aerial  Tides. — 
Of  Sound  in  General. — Of  Sonorous  Bodies. — Of 
Musical  Sounds. — Of  Concord  or  Harmony,  and 
Melody. 

MRS.  B.  Well,  Caroline,  have  you  ascertained 
what  kind  of  pump  you  have  in  yourj^arden  ? 

Caroline.  1  think  it  must  be  merely  a  lifting- 
pump,  because  no  more  force  is  required  to  raise  the 
handle  than  is  necessary  to  lift  its  weight  :  and  in  a 
forcing-pump,  by  raising  the  handle,  you  force  the 
water  into  the  smaller  pipe,  and  the  resistance  the 
water  offers  must  require  an  exertion  of  strength  to 
overcome  it. 

Mrs.  B.  I  make  no  doubt  you  are  right ;  for  lift- 
ing pumps,  being  simple  in  their  construction,  are  by 
far  the  most  common. 

1  have  promised  to  day  to  give  you  some  account 
of  the  nature  of  wind.  Wind  is  nothing  more  than 
the  motion  of  a  stream  or  current  of  air,  generally 
produced  by  a  partial  change  of  temperature  in  the 
atmosphere  ;  for  when  any  one  part  is  more  heated 
than  the  rest,  that  part  is  rarefied  ;  the  equilibrium  is 
destroyed,  and  the  air  in  consequence  rises.  When 
this  happens,  there  necessarily  follows  a  motion  of  the 
surrounding  air  towards  that  part,  in  order  to  re- 
store it ;    this  spot,  therefore,  receives  winds  from 


t>N  WIND  AND  SOUND.  18l 

every  quarter.  Those  who  live  to  the  north  of  it  ex- 
perience a  north  wind  ;  those  to  the  south,  a  south 
wind  ; — do  you  comprehend  this  ? 

Caroline  Perfectly.  But  what  sort  of  weather 
must  those  people  have,  who  live  on  the  spot  where 
ihese  winds  meet  and  interfere  ? 

Mrs.  B.  They  have  turbulent  and  boisterous 
weather,  whirlwinds,  hurricanes,  rain,  lightning, 
thunder,  &c.  This  stormy  weather  occurs  most  fre- 
quently in  the  torrid  zone,  where  the  heat  is  greatest : 
the  air  being  more  rarefied  there  than  m  any  other 
part  of  the  ^lobe,  is  lighter,  and  consequently  ascends  ', 
whilst  the  air  about  the  polar  regions  is  continually 
flowing  from  the  poles,  to  restore  the  equilibrium. 

Caroline.  This  motion  of  the  air  would  produce  a 
regular  and  constant  north  wind  to  the  inhabitants  of 
the  northern  hemisphere  ;  and  a  south  wind  to  those 
of  the  southern  hemisphere,  and  continual  storms  at 
the  equator,  where  these  two  adverse  winds  would 
meet. 

Mrs.  B.  These  winds  do  not  meet,  for  they  each 
change  their  direction  before  they  reach  the  equator. 
The  sun,  in  moving  over  the  equatorial  regions  from 
east  to  west,  rarefies  the  air  as  it  passes,  and  causes 
the  denser  eastern  air  to  flow  westwards,  in  order  to 
restore  the  equilibrium  ;  thus  producing  a  regular 
east  wind  about  the  equator. 

Caroline.  The  air  from  the  west,  then,  constantly 
goes  to  meet  the  sun,  and  repair  the  disturbance 
which  his  beams  have  produced  in  the  equilibrium  of 
the  atmosphere.  But  1  wonder  how  you  will  recon- 
cile these  various  winds,  Mrs.  B.  :  you  first  led  me 
to  suppose  there  was  a  constant  struggle  between  op- 
posite winds  at  the  equator,  producing  storm  and 
tempest ;  but  now  1  hear  of  one  regular  invariable 
wind,  which  must  naturally  be  attended  by  calm 
weather. 

Emily.  I  think  I  comprehend  it :  do  not  these 
winds  from  the  north  and  south  combine  with  the 
16 


182  ON  WIND  AND  SOUND. 

easterly  wind  about  the  equator,  and  form  what  are 
called  the  trade-winds  ? 

Mrs.  B.  Just  so,  my  dear.  The  composition  of 
the  two  winds  nortli  and  east,  produces  a  constant 
north-east  wind  ;  and  that  of  the  two  winds  south  and 
east,  produces  a  regular  south-east  wind  :  these  winds 
extend  to  about  thirty  degrees  on  each  side  of  the 
equator,  the  regions  further  distant  from  it  expe- 
riencing only  their  respective  north  and  south  winds. 

Caroline.  But,  Mrs.  B.,  if  the  air  is  constantly 
flowing  from  the  poles  to  the  torrid  zone,  there  must 
be  a  deficiency  of  air  in  the  polar  regions  ? 

Mrs.  B.  The  light  air  about  the  equator,  which  ex- 
pands and  rises  into  the  upper  regions  of  the  atmos- 
phere, ultimately  flows  from  thence  back  to  the  poles 
to  restore  the  equilibrium  :  if  it  were  not  for  this  re- 
source, the  polar  atmospheric  regions  would  soon  be 
exhausted  by  the  stream  of  air,  which,  in  the  lower 
strata  of  the  atmosphere,  they  are  constantly  sending 
towards  the  equator. 

Carolitie.  There  is  then  a  sort  of  circulation  of 
air  in  the  atmosphere  ;  the  air  in  the  lower  strata 
flowing  from  the  poles  towards  the  equator,  and  in 
the  upper  strata,  flowing  back  from  the  equator  to- 
wards the  poles. 

Mrs.  B.  Exactly  :  I  can  show  you  an  example  of 
this  circulation  on  a  small  scale.  The  air  of  this 
room  being  more  rarefied  than  the  external  air,  a 
wind  or  current  of  air  is  pouring  in  from  the  crevices 
of  the  windows  and  doors,  to  restore  the  equilibrium  ; 
but  the  light  air  with  which  the  room  is  filled  must 
find  some  vent,  in  order  to  make  way  for  the  heavy 
air  which  enters.  If  you  set  the  door  a-jar,  and  hold 
a  candle  near  the  upper  part  of  it,  you  will  find  that 
the  flame  will  be  blown  outwards,  showing  that  there 
is  a  current  of  air  flowing  out  from  the  upper  part  of 
the  room. — Now  place  the  candle  on  the  floor  close 
by  the  door,  and  you  will  perceive,  by  the  inclination 
of  the  flame,  that  there  is  also  a  current  of  air  setting 
into  the  room. 


ON    WIND   AND    SOUND.  183 

Caroline.  It  is  just  so  ;  the  upper  current  is  the 
warm  light  air,  which  is  driven  out  to  make  way  for 
the  stream  of  cold  dense  air  which  enters  the  room 
lower  down. 

Emily.  I  have  heard,  Mrs.  B.,  that  the  periodical 
winds  are  not  so  regular  on  land  as  at  sea  :  what  is  the 
reason  of  that  ? 

Mrs.  B.  The  land  reflects  into  the  atmosphere  a 
much  greater  quantity  of  the  sun's  rays  than  the  wa- 
ter ;  therefore,  that  part  of  the  atmosphere  which  is 
over  the  land,  is  more  heated  and  rarefied  than  that 
which  is  over  the  sea  :  this  occasions  the  wind  to  set 
in  upon  the  land,  as  we  find  that  it  regularly  does  on 
the  coast  of  Guinea,  and  other  countries  in  the  torrid 
zone. 

Emily.  I  have  heard  much  of  the  violent  tempests 
occasioned  by  the  breaking  up  of  the  monsoons  ;  are 
not  they  also  regular  trade-winds  ? 

Mrs.  B.  They  are  called  periodical  trade-winds, 
as  they  change  their  course  every  half  year.  This 
variation  is  produced  by  the  earth's  annual  course 
round  the  sun,  when  the  north  pole  is  inclined  towards 
that  luminary  one  half  of  the  year,  the  south  pole 
the  other  half.  During  the  summer  of  the  northern 
hemisphere,  the  countries  of  Arabia,  Persia,  India 
and  China,  are  much  heated,  and  reflect  great  quan- 
tities of  the  sun's  rays  into  the  atmosphere,  by  which 
it  becomes  extremely  rarefied,  and  the  equilibrium 
consequently  destroyed.  In  order  to  restore  it,  the 
air  from  the  equatorial  southern  regions,  where  it  is 
colder,  (as  well  as  from  the  colder  northern  parts,) 
must  necessarily  have  a  motion  towards  those  parts. 
The  current  of  air  from  the  equatorial  regions  pro- 
duces the  trade-winds  for  the  first  six  months,  in  all 
the  seas  between  the  heated  continent  of  Asia,  and  the 
equator.  The  other  six  months,  when  it  is  summer 
in  the  southern  hemisphere,  the  ocean  and  countries 
towards  the  southern  tropic  are  most  heated,  and  the 
air  over  those  parts  most  rarefied  :  then  the  air  about 


it84  ON    WIND    AND    SOUND. 

flhe  equator  alters  iis  course,  and  flows  exactly  in  an 
•pposite  direction. 

Caroline.  This  explanation  of  the  monsoons  is  very 
ourious  ;  but  what  does  their  breaking  up  mean  ? 

Mrs,  B.  It  is  the  name  given  by  sailors  to  the 
shifting  of  the  periodical  winds  ;  they  do  not  change 
their  course  suddenly,  but  by  degrees,  as  the  sun 
moves  from  one  hemisphere  to  the  other  :  this  change 
is  usually  attended  by  storms  and  hurricanes,  very 
dana^erous  for  shipping  ;  so  that  those  seas  are  sel- 
dom navigated  at  the  season  of  the  equinox. 

Etniiy.  1  think  I  understand  the  winds  in  the  tor- 
rid zone  perfectly  well  ;  but  what  is  it  that  occasions 
the  great  variety  of  winds  which  occur  in  the  tempe- 
rate zones  ?  for,  according  to  your  theory,  there 
should  be  only  north  and  south  winds  in  those  cli- 
mates. 

Mrs.  B.  Since  so  large  a  portion  of  the  atmos- 
phere as  is  over  the  torrid  zone  is  in  continued  agi- 
tation, these  agitations  in  an  elastic  fluid,  which  yields 
to  the  slightest  impression,  must  extend  every  way  to 
a  great  distance  ;  the  air,  therefore,  in  all  climates, 
will  suff"er  more  or  less  perturbation,  according  to  the 
situation  of  the  country,  the  position  of  mountains,  val- 
leys, and  a  variety  of  other  causes  :  hence  it  is  easy 
to  conceive,  that  almost  every  climate  must  be  liable 
to  variable  winds. 

On  the  seashore,  there  is  almost  always  a  gentle 
sea-breeze  setting  in  on  the  land  on  a  summer's  even- 
ing, to  restore  the  equilibrium  which  has  been  dis- 
turbed by  reflections  from  the  heated  surHice  of  the 
shore  during  the  day  ;  and  when  night  has  cooled  the 
land,  and  condensed  the  air,  we  generally  find  it,  to- 
wards morning,  flowing  back  towards  the  sea. 

Caroline.  I  have  observed,  that  the  wind,  which- 
ever way  it  blows,  almost  always  falls  about  sunset  ? 

Mrs.  B.  Because  the  rarefaction  of  air  in  the  par- 
ticular spot  which  produces  the  wind,  diminishes  as 
the  sun  declines,  and  consequently  the  velocity  of  the 
wind  abates. 


ON  WIND  AND  SOUND*  1 8^ 

Emily.  Since  the  air  is  a  gravitating  fluid,  is  it  not 
affected  by  the  attraction  of  the  moon  and  the  sun,  ia 
the  same  manner  as  the  waters  ? 

Mrs.  B.  Undoubtedly ;  but  the  aerial  tides  are  as 
much  greater  than  those  of  water,  as  the  density  of 
water  exceeds  that  of  air,  which,  as  you  may  recol- 
lect, we  found  to  be  about  800  to  1. 

Caroline.  What  a  prodigious  protuberance  that 
must  occasion!  How  much  the  weight  of  such  a  co- 
lumn of  air  must  raise  the  mercury  in  the  barometer? 

Emily.  As  this  enormous  tide  of  air  is  drawn  up 
and  supported,  as  it  were,  by  the  moon,  its  weight 
and  pressure,  I  should  suppose,  would  be  rather  di- 
minished than  increased  ? 

Mrs.  B.  The  weight  of  the  atmosphere  is  neither 
increased  nor  diminished  by  the  aerial  tides.  The 
moon's  attraction  augments  the  bulk  as  much  as  it  di- 
minishes the  weight  of  the  column  of  air ;  these  ef- 
fects, therefore,  counterbalancing  each  other,  the 
aerial  tides  do  not  affect  the  barometer. 

Caroline.     I  do  not  quite  understand  that. 

Mrs.  B.  Let  us  suppose  that  the  additional  bulk  of 
air  at  high  tide  raises  the  barometer  one  inch ;  and  on 
the  other  hand,  that  the  support  which  the  moon's 
attraction  affords  the  air  diminishes  its  weight  or  pres- 
sure, so  as  to  occasion  the  mercury  to  fall  one  inch  ; 
under  these  circumstances  the  mercury  must  remain 
stationary.  Thus  you  see,  that  we  can  never  be  sen- 
sible of  aerial  tides  by  the  barometer,  on  account  of 
the  equality  of  pressure  of  the  atmosphere,  whatever 
be  its  height. 

The  existence  of  aerial  tides  is  not,  however,  hy- 
pothetical ;  it  is  proved  by  the  effect  they  produce  on 
the  apparent  position  of  the  heavenly  bodies ;  but  this 
I  cannot  explain  to  you,  till  you  understand  the  pro- 
perties of  light. 

Emily.     And  when  shall  we  learn  them  ? 

Mr. .  B.     1  shall  first  explain  to  you  the  nature  of 
sound,  which  is  intimately  connected  with  that  of  airj 
16* 


18C  ON  WIND  AND  SOUND. 

and  I  think  at  our  next  meeting  we  may  enter  upon 
the  subject  of  optics. 

We  have  now  considered  the  effects  produced  by 
the  wide  and  extended  agitation  of  the  air ;  but  there 
is  another  kind  of  agitation  of  which  the  air  is  suscep- 
tible— a  sort  of  vibratory  trembling  motion,  which, 
striking  on  the  drum  of  the  ear,  produces  sound. 

Caroline.  Is  not  sound  produced  by  soHd  bodies  ? 
The  voice  of  animals,  the  ringing  of  bells,  musical 
instruments,  are  all  solid  bodies.  I  know  of  no  sound 
"but  that  of  the  wind  which  is  produced  by  the  air. 

Mrs.  B.  Sound,  I  assure  you,  results  from  a  tre- 
mulous motion  of  the  air ;  and  the  sonorous  bodies 
you  enumerate  are  merely  the  instruments  by  which 
that  peculiar  species  of  motion  is  communicated  to 
the  air. 

Caroline.  What!  when  I  ring  this  little  bell,  is  it 
the  air  that  sounds,  and  not  the  bell? 

Mrs.  B.  Both  the  bell  and  the  air  are  concerned 
in  the  production  of  sound.  But  sound,  strictly 
Speaking,  is  a  perception  excited  in  the  mind  by  the 
motion  of  the  air  on  the  nerves  of  the  ear  ;  the  air, 
therefore,  as  well  as  the  sonorous  bodies  which  put 
it  in  motion,  is  only  the  cause  of  sound,  the  immediate 
effect  is  produced  by  the  sense  of  hearing ;  for,  with- 
out this  sense,  there  would  be  no  sound. 

Emily.  I  can  with  difl&culty  conceive  that.  A  per- 
son born  deaf,  it  is  true,  has  no  idea  of  sound,  be- 
cause he  hears  none  :  yet  that  does  not  prevent  the 
peal  existence  of  sound,  as  all  those  who  are  not  deaf 
can  testify. 

Mrs.  B.  I  do  not  doubt  the  existence  of  sound  to 
all  those  who  possess  the  sense  of  hearing ;  but  it 
exists  neither  in  the  sonorous  body  nor  in  the  air,  but 
in  the  mind  of  the  person  whose  ear  is  struck  by  the 
vibratory  motion  of  the  air,  produced  by  a  sonorous 
body. 

To  convince  you  that  sound  does  not  exist  in  sono- 
cous  bodies,  but  that  air  or  some  other  vehicle  is  ne- 
tressary  to  its  production,  endeavour  to  ring  the  little 


ON  WIND  AUD  SOUND.  18^ 

bell,  after  I  have  suspended  it  under  a  receiver  in  the 
air-pump,  from  which  I  shall  exhaust  the  air 

Caroline.  This  is  indeed  very  strange  :  though  I 
agitate  it  so  violently,  it  does  not  produce  the  least 
sound. 

Mrs.  B.  By  exhausting  the  receiver,  1  have  cut 
off  the  communication  between  the  air  and  the  bell ; 
the  latter,  therefore,  cannot  impart  its  motion  to  the 
air. 

Caroline.  Are  you  sure  that  it  is  not  the  glass, 
which  covers  the  bell,  that  prevents  our  hearing  it  ? 

Mrs.  B.  That  you  may  easily  ascertain  by  letting 
the  air  into  the  receiver,  and  then  ringing  the  bell. 

Caroline.  Very  true  :  I  can  hear  it  now  almost  as 
loud  as  if  the  glass  did  not  cover  it  ;  and  I  can  no 
longer  doubt  but  that  air  is  necessary  to  the  produc- 
tion of  sound. 

Airs.  B.  Not  absolutely  necessary,  though  by  far 
the  most  common  vehicle  of  sound.  Liquids,  as  well 
as  air,  are  capable  of  conveying  the  vibratory  motion 
of  a  sonorous  body  to  the  organ  of  hearing  ;  as  sound 
can  be  heard  under  water.  Solid  bodies  also  convey 
sound,  as  I  can  soon  convince  you  by  a  very  simple 
experiment.  I  shall  fasten  this  string  by  the  middle 
round  the  poker ;  now  raise  the  poker  from  the 
ground  by  the  two  ends  of  the  string,  and  hold  one  to 
each  of  your  ears  : — I  shall  now  strike  the  poker  with 
a  ke}^  and  you  will  find  that  the  sound  is  conve3'ed  to 
the  ear  by  means  of  the  strings,  in  a  much  more  per- 
fect manner  than  if  it  had  no  other  vehicle  than  the 
air. 

Caroline.  That  it  is,  certainly,  for  I  am  almost 
stunned  by  the  noise.  But  what  is  a  sonorous  body, 
Mrs.  B.  ?  for  all  bodies  are  capable  of  producing 
some  kind  of  sound  by  the  motion  they  communicate 
to  the  air. 

Mrs.  B.  Those  bodies  are  called  sonorous,  which 
produce  clear,  distinct,  regular,  and  durable  sounds, 
such  as  a  bell,  a  drum,  musical  strings,  wind-instru- 
ments, &c.     They  owe  this  property  to  their  elasti* 


188  ©N  WIND  AND  SOUND. 

city  ;  for  an  elastic  body,  after  having  been  struck, 
not  only  returns  to  its  former  situation,  but  having 
acquired  momentum  by  its  velocity,  like  the  pendu- 
lum, it  springs  out  on  the  opposite  side.  If  1  draw 
the  string  A  B,  which  is  made  fast  at  both  ends  to  C, 
it  will  not  only  return  to  its  original  position,  but  pro- 
ceed onwards  to  D.  This  is  its  first  vibration,  at  the 
end  of  which  it  will  retain  sufficient  velocity  to  bring 
it  to  E,  and  back  again  to  F,  which  constitutes  its  se- 
cond vibration  ;  the  third  vibration  will  carry  it  only 
to  G  and  H,  and  so  on,  till  the  r^istance  of  the  air 
destroys  its  motion. 

The  vibration  of  a  sonorous  body  gives  a  tremu- 
lous motion  to  the  air  around  it,  very  similar  to  the 
motion  communicated  to  smooth  water  when  a  stone 
is  thrown  into  it.  This  first  produces  a  small  circu- 
lar wave  around  the  spot  in  which  the  stone  falls  j 
the  wave  spreads,  and  gradually  communicates  its 
motion  to  the  adjacent  waters,  producing  similar 
waves  to  a  considerable  extent.  The  same  kind  of 
waves  are  produced  in  the  air  by  the  motion  of  a 
sonorous  body,  but  with  this  difference,  that  as  air  is 
an  elastic  fluid,  the  motion  does  not  consist  of  regu- 
larly extending  waves,  but  of  vibrations,  and  are  com- 
posed of  a  motion  forwards  and  backwards,  similar  to 
those  of  the  sonorous  body.  They  differ  also  in  the 
one  taking  place  in  a  plane,  the  other  in  all  direc- 
tions.    The  aerial  undulations  being  spherical. 

Emily.  But  if  the  air  moves  backwards  as  well  as 
forwards,  how  can  its  motion  extend  so  as  to  convey 
sound  to  a  distance  ? 

Mrs.  B.  The  first  sphere  of  undulations  which 
are  produced  immediately  around  the  sonorous  body, 
by  pressing  against  the  contiguous  air,  condenses  it. 
The  condensed  air,  though  impelled  forward  by  the 
pressure,  re-acts  on  the  first  set  of  undulations,  dri- 
ving them  back  again.  The  second  set  of  undula- 
tions which  have  been  put  in  motion,  in  their  turn 
communicate  their  motion,  and  are  themselves  driven 
back  by  re-action.    Thus  there  is  a  succession  of 


v>N  WIx\D  AND  SOUNE».  18& 

waves  in  the  air,  corresponding  with  the  succession 
©f  waves  in  the  water. 

Caroline.  The  vibrations  of  sound  must  extend 
much  further  than  the  circular  waves  in  water,  since 
sound  is  conveyed  to  a  great  distance. 

Mrs.  B.  The  air  is  a  fluid  so  much  less  dense 
than  water,  that  motion  is  more  easily  communicated 
to  it.  The  report  of  a  cannon  produces  vibrations 
of  the  air,  which  extend  to  several  miles  around. 

Emily.  Distant  sound  takes  some  time  to  reach 
us,  since  it  is  produced  at  the  moment  the  cannon  is 
fired  ;  and  we  see  the  light  of  the  flash  long  before 
we  hear  the  report. 

Mrs.  B.  The  air  is  immediately  put  in  motion  by 
the  firing  of  a  cannon  ;  but  it  requires  time  for  the 
vibrations  to  extend  to  any  distant  spot.  The  veloci- 
ty of  sound  is  computed  to  be  at  the  rate  of  1142 
feet  in  a  second. 

Caroline.  With  what  astonishing  rapidity  the  vi- 
brations must  be  communicated  !  But  the  velocity  of 
sound  varies,  I  suppose,  with  that  of  the  air  which 
conveys  it.  If  the  wind  sets  towards  us  from  the 
cannon,  we  must  hear  the  report  sooner  that  if  it  set 
the  other  waj'. 

Mrs.  B.  The  direction  of  the  wind  makes  less  difl*er- 
ence  in  the  velocity  of  sound  than  you  would  imagine, 
if  the  wind  sets  from  us,  it  bears  most  of  the  aerial 
waves  away,  and  renders  the  sound  fainter  ;  but  it  is 
not  very  considerably  longer  in  reaching  the  ear  than 
if  the  wind  blew  towards  us.  This  uniform  velocity 
of  sound  enables  us  to  determine  the  distance  of  the 
object  trom  which  it  proceeds  ;  as  that  of  a  vessel  at 
sea  firing  a  cannon,  or  that  of  a  thunder  cloud.  If 
we  do  no  not  hear  the  thunder  till  half  a  minute  after 
we  see  the  lightning,  we  conclude  the  cloud  to  be  at 
the  distance  of  six  miles  and  a  half. 

Emily.  Pray  how  is  the  sound  of  an  echo  pro- 
duced ? 

Mrs.  B.  When  the  aerial  vibrations  meet  with  an 
obstacle,  having  a  hard  and  regular  surface,  such  as  a 


190  ON  WIND  AND  SOUND. 

wall,  or  rock,  they  are  reflected  back  to  the  ear,  and 
produce  the  same  sound  a  second  time  ;  but  the  sound 
will  then  appear  to  proceed  from  the  object  by  which 
it  is  reflected.  If  the  vibrations  fall  perpendicularly 
on  the  obstacle,  they  are  reflected  back  in  the  same 
line  ;  if  obliquely,  the  sound  returns  obliquely  in  the 
opposite  direction,  the  angle  of  reflection  being 
equal  to  the  angle  of  incidence 

Caroline.  Oh,  then,  Emily,  I  now  understand  why 
the  echo  of  my  voice  behind  our  house  is  heard  so 
much  plainer  by  you  than  it  is  by  me,  when  we  stand 
at  the  opposite  ends  of  the  gravel  walk.  My  voice, 
or  rather,  1  should  say,  the  vibrations  of  air  it  occa- 
sions, fall  obliquely  on  the  wall  of  the  house,  and 
are  reflected  by  it  to  the  opposite  end  of  the  gravel 
walk. 

Emily.  Very  true  ;  and  we  have  observed,  that 
when  we  stand  in  the  middle  of  the  walk,  opposite 
the  house,  the  echo  returns  to  the  person  who  spoke. 

Mrs.  B.  Speaking-trumpets  are  constructed  on  the 
principle  of  the  reflection  of  sound.  The  voice,  instead 
ofbeingdiff'usedinthe  open  air,  is  confined  within  the 
trumpet ;  and  the  vibrations,  which  spread  and  fall 
against  the  sides  of  the  instrument,  are  reflected  ac- 
cording to  the  angle  of  incidence,  and  fall  into  the  direc- 
tion of  the  vibrations  which  proceed  straight  forwards. 
The  whole  of  the  vibrations  are  thus  collected  into  a 
focus  ;  and  if  the  ear  be  situated  in  or  near  thkt  spot, 
the  sound  is  prodigiously  increased.  Figure  7.  Plate 
XIV.  will  give  you  a  clearer  idea  of  the  speaking- 
trumpet  :  the  reflected  rays  are  distinguished  from 
those  of  incidence,  by  being  dotted  ;  and  they  are 
brought  to  a  focus  at  F.  The  trumpet  used  by  deaf 
persons  acts  on  the  same  principle  ;  but  as  the  voice 
enters  the  trumpet  at  the  large,  instead  of  the  small 
end  of  the  instrument,  it  i?  not  so  much  confined,  nor 
the  sound  so  much  increased. 

Emily.   Are    the  trumpets  used  as  musical  instru- 
ments also  constructed  on  this  principle  ? 

Mrs.  B.     So  far  as  their  form  tends  to  increase  the 


V 

ON  WIND  AND  SOUNIK  191 

sound,  they  are  ;  but,  as  a  musical  instrument,  the 
trumpet  becomes  itself  the  sonorous  body,  which  is 
made  to  vibrate  by  blowing  into  it,  and  communicates 
its  vibrations  to  the  air. 

I  will  attempt  to  give  you,  in  a  few  words,  some  no- 
tion of  the  nature  of  musical  sounds,  which,  as  you 
are  fond  of  music,  must  be  interesting  to  you. 

if  a  sonorous  body  be  struck  in  such  a  manner, 
that  its  vibrations  are  all  performed  in  regular  times, 
the  vibrations  of  the  air  will  correspond  with  them  ; 
and  striking  in  the  same  regular  manner  on  the  drum 
of  the  ear,  will  produce  the  same  uniform  sensation  on 
the  auditory  nerve,  and  excite  the  same  uniform  idea 
in  the  mind  ;  or,  in  other  words,  we  shall  hear  one 
musical  tone. 

But  if  the  vibrations  of  the  sonorous  body  are  irre- 
gular, there  will  necessarily  follow  a  confusion  of  aeri- 
al vibrations  ;  for  a  second  vibration  may  commence 
before  the  first  is  finished,  to  meet  it  half  way  on  its 
return,  interrupt  it  in  its  course,  and  produce  harsh 
jarring  sounds,  which  are  called  discords. 

Emily.  But  each  set  of  these  irregular  vibrations, 
if  repeated  at  equal  intervals,  would,  1  suppose,  pro- 
duce a  musical  tone  ?  It  is  only  their  irregular  suc- 
cession which  makes  them  interfere,  and  occasions 
discord. 

Mrs  B.  Certainly.  The  quicker  a  sonorous  bo- 
dy vibrates,  the  more  acute,  or  sharp,  is  the  sound 
produced. 

Caroline.  But  if  I  strike  any  one  note  of  the  piano- 
forte repeatedly,  whether  quickly  or  slowly,  it  al- 
ways gives  the  same  tone. 

Mrs.  B.  Because  the  vibrations  of  the  same 
string  at  the  same  degree  of  tension,  are  always  of  a 
similar  duration.  The  quickness  or  slowness  of  the 
vibrations  relate  to  the  single  tones,  not  to  the  vari- 
ous sounds  which  they  may  compose  by  succeeding 
each  other.  Striking  the  note  in  quick  succession, 
produces  a  more  frequent  repetition  of  the  tone,  but 
does  not  increase  tlie  velocity  of  the  vibrations  of  the 


192  ONT  WIND  AND  30UND. 

string.  The  duration  of  the  vibrations  of  strings  or 
chords,  depends  upon  their  length,  their  thickness  or 
weight,  and  their  degree  of  tension  :  thus,  you  find, 
the  low  bass  notes  are  produced  by  long,  thick,  loose 
strings  ;  and  the  high  treble  notes  by  short,  small,  and 
tight  strings. 

Caroline.  Then  the  different  length  and  size  of 
the  strings  of  musical  instruments,  serves  to  vary  the 
duration  of  the  vibrations,  and  consequently,  the 
acuteness  or  gravity  of  the  notes  ? 

Mrs.  B.  Yes.  Among  the  variety  of  tones,  there 
are  some  which,  sounded  together,  please  the  ear, 
producing  what  we  call  harmony,  or  concord.  This 
arises  from  the  agreement  of  the  vibrations  of  the 
two  sonorous  bodies  ;  so  that  some  of  the  vibrations 
of  each  strike  upon  the  ear  at  the  same  time.  Thus,  if 
the  vibrations  of  two  strings  are  performed  in  equal 
times,  the  same  tone  is  produced  by  both,  and  they 
are  said  to  be  in  unison. 

Emily.  Now,  then,  I  understand  why,  when  I 
tune  my  harp  in  unison  with  the  piano-forte,  I  draw 
the  strings  tighter  if  it  is  too  low,  or  loosen  them  if  it 
is  at  too  high  a  pitch  ;  it  is  in  order  to  bring  them  to 
vibrate,  in  equal  times,  with  the  strings  of  the  piano- 
forte. 

J\Jrs.  B.  But  concord,  you  know,  is  not  confined 
to  unison  ;  for  two  different  tones  harmonize  in  a  va- 
riety of  cases.  If  the  vibrations  of  one  string  (or 
sonorous  body  whatever)  vibrate  in  double  the  time 
of  another,  the  second  vibration  of  the  latter  will 
strike  upon  the  ear  at  the  same  instant  as  the  first  vi- 
bration of  the  former  ;  and  this  is  the  concord  of  an 
octave. 

If  the  vibrations  of  two  strings  are  as  two  to 
three,  the  second  vibration  of  the  first  corresponds 
with  the  third  vibration  of  the  latter,  producing  the 
harmony  called  a  fifth. 

Caroline.  So,  then,  when  I  strike  the  key-note 
with  its  fifth,  I  hear  every  second  vibration  of  one, 
and  every  third  of  the  other  at  the  same  time  ? 


ON  WIND  AND  SOUN».  10^ 

Mrs.  B.  Yes  ;  and  the  key-note  struck  with  the 
fourth  is  likewise  a  concord,  hecause  the  vibrations 
are  as  three  to  four.  The  vibrations  of  a  major  third 
with  the  key-note,  are  as  four  to  tive  ;  and  those  of 
a  minor  third,  as  five  to  six. 

There  are  other  tones  which,  though  they  cannot 
be  struck  together  without  producing  discord,  if 
struck  successively  give  us  the  pleasure  which  is  call- 
ed melody.  Upon  these  general  principles  the  sci- 
ence of  music  is  founded  ;  but  I  am  not  sufliciently 
acquainted  with  it  to  enter  any  further  into  it. 

We  shall  now,  therefore,  take  leave  of  the  subject 
of  sound  ;  and,  at  our  next  interview,  enter  upon 
that  of  optics,  in  which  we  shall  consider  the  nature 
of  vision,  light,  and  colours. 


17 


CONVERSATION  XIV, 


ON  OPTICS. 

Of  Luminous,  Transparent,  and  Opaque  Bodies. — Of 
the  Radiation  of  Light. — Of  Shadows. — Of  the  Re- 
flection of  Light. — Opaque  Bodies  seen  only  by  Re- 
fleeted  Light. — Vision  Explained. — Camera  ObscU' 
ra. — Image  of  Objects  on  the  Retina. 

CAROLINE.  I  long  to  begin  our  lesson  to  day, 
Mrs.  B.,  for  1  expect  that  it  will  be  very  entertaining. 

Mrs.  B.  Optics  is  certainly  one  of  the  most  in- 
teresting branches  of  Natural  Philosophy,  but  not  one 
of  the  easiest  to  understand  ;  I  must  therefore  beg 
that  you  will  give  me  the  whole  of  your  attention. 

I  shall  first  inquire,  whether  you  comprehend  the 
meaning  of  a  luminous  body,  an  opaque  body,  and  a 
transparent  body. 

Caroline.  A  luminous  body  is  one  that  shines  ;  an 
opaque  .  .  . 

Mrs.  B.  Do  not  proceed  to  the  second,  until  we 
have  agreed  upon  the  definition  of  the  first.  All  bo- 
dies that  shine  are  not  luminous  ;  for  a  luminous  body 
is  one  that  shines  by  its  own  light,  as  the  sun,  the  fire, 
a  candle,  &c. 

Emily.  Polished  metal  then,  when  it  shines  with 
so  much  brilliancy,  is  not  a  luminous  body  ? 

Mrs.  B.  No,  for  it  wouM  be  dark  if  it  did  not  re- 
ceive light  from  a  luminous  body  ;  it  belongs,  there- 
fore, to  the  class  of  opaque  or  dark  bodies,  which 


Fig.   1. 


fzatJ^ 


^   ^^ 


ON  OPTICS.  195 

comprehend  all  such  as  are  neither  luminous  nor  will 
admit  the  light  to  pass  through  them. 

Emily.  And  transparent  bodies  are  those  which 
admit  the  light  to  pass  through  them  ;  such  as  glass 
and  water  ? 

Mrs.  B»  You  are  right.  Transparent  or  pellucid 
bodies  are  frequently  called  mediums  ;  and  the  rays 
of  light  which  pass  through  them  are  said  to  be 
transmitted  by  them. 

Light,  when  emanated  from  the  sun,  or  any  other 
luminous  body,  is  projected  forwards  in  straight  lines 
in  every  possible  direction  :  so  that  the  luminous 
body  is  not  only  the  general  centre  from  whence  all 
the  rays  proceed  ;  but  every  point  of  it  may  be  con- 
sidered as  a  centre  which  radiates  light  in  every  di- 
rection.    (Fig.  1.  Plate  XV.) 

Emily.  But  do  not  the  rays  which  are  projected 
in  different  directions,  and  cross  each  other,  interfere 
and  impede  each  other's  course  ? 

Mrs.  B.  Not  at  all.  The  particles  of  light  are  so 
extremely  minute,  that  they  are  never  known  to  in- 
terfere with  each  other.  A  ray  of  light  is  a  single 
line  of  light  projected  from  a  luminous  body  ;  and  a 
pencil  of  rays  is  a  collection  of  rays  proceeding  from 
any  one  point  of  a  luminous  body,  as  fig.  2. 

Caroline.  Is  light  then  a  substance  composed  of 
particles  like  other  bodies  ? 

Mrs.  B.  That  is  a  disputed  point  upon  which  I 
cannot  pretend  to  decide.  In  some  respects,  light  is 
obedient  to  the  laws  which  govern  bodies  ;  in  others, 
it  appears  to  be  independent  of  them  ;  thus,  though 
its  course  is  guided  by  the  laws  of  motion,  it  does 
not  seem  to  be  influenced  by  those  of  gravity.  It 
has  never  been  discovered  to  have  weight,  though  a 
variety  of  interesting  experiments  have  been  made 
with  a  view  of  ascertaining  that  point ;  but  we  are 
so  ignorant  of  the  intimate  nature  of  light,  that  an  at- 
tempt to  investigate  it  would  lead  us  into  a  labyrinth 
of  perplexity,  if  not  of  error  ;  we  shall  therefore 


196  ON  OPTICS. 

i5onfine    our  attention  to  those  properties  of  light 
which  are  well  ascertained. 

Let  us  return  to  the  examination  of  the  effects  of 
the  radiation  of  light  from  a  luminous  body.  Since 
the  rays  of  light  are  projected  in  straight  lines,  when 
they  meet  with  an  opaque  body  through  which  they 
are  unable  to  pass,  they  are  stopped  short  in  their 
course  ;  for  they  cannot  move  in  a  curve  line  round 
the  body. 

Caroline.  No,  certainly  ;  for  it  would  require 
some  other  force  besides  that  of  projection  to  pro- 
duce motion  in  a  curve  line. 

Mrs.  B.  The  interruption  of  the  rays  of  light,  by 
the  opaque  body,  produces,  therefore,  darkness  on 
the  opposite  side  of  it  ;  and  if  this  darkness  fall  upon 
a  wall,  a  sheet  of  paper,  or  any  object  whatever,  it 
forms  a  shadow. 

Emily.  A  shadow  then,  is  nothing  more  than 
darkness  produced  by  the  intervention  of  an  opaque 
body,  which  prevents  the  rays  of  light  from  reaching 
an  object  behind  the  opaque  body. 

Caroline.  Why  then  are  shadows  of  different  de- 
grees of  darkness  ;  for  I  should  have  supposed  from 
your  definition  of  a  shadow,  that  it  would  have  been 
perfectly  black  ? 

Mrs.  B.  It  frequently  happens  that  a  shadow  is 
produced  by  an  opaque  body  interrupting  the  course 
of  the  rays  from  one  luminous  body,  while  light 
from  another  reaches  the  space  where  the  shadow  is 
formed,  in  which  case  the  shadow  is  proportionally 
fainter.  This  happens  if  the  opaque  body  be  lighted 
by  two  candles  :  if  you  extinguish  one  of  them,  the 
shadow  will  be  both  deeper  and  more  distinct. 

Caroline.     But  yet  it  will  not  be  perfectly  dark. 

Mrs.  B.  Because  it  is  still  slightly  illumined  by 
light  reflected  from  the  walls  of  the  room,  and  other 
surrounding  objects. 

You  must  observe,  also,  that  when  a  shadow  is 
produced  by  the   interruption  of  rays  from  a  single 


ON  OPTICS.  197 

luminous  body,  the  darkness  is  proportional  to  the 
intensity  of  the  light. 

Emily.  I  should  have  supposed  the  contrary  ;  for 
as  the  light  reflected  from  surrounding  objects  on  the 
shadow,  must  be  in  proportion  to  the  intensity  of  the 
light,  the  stronger  tlie  light  the  more  the  shadow 
will  be  illumined. 

Mrs.  B.  Your  remark  is  perfectly  just  ;  but  as 
we  have  no  means  of  estimating  the  degrees  of  light 
and  of  darkness  but  by  comparison,  the  strongest 
light  will  appear  to  produce  the  deepest  shadow. — 
Hence  a  total  eclipse  of  the  sun  occasions  a  more  sen- 
sible darkness  than  midnight,  as  it  is  immediately 
contrasted  with  the  strong  light  of  noonday. 

Caroline.  The  re-appearance  of  the  sun  after  an 
eclipse  must,  by  the  same  contrast,  be  remarkably 
brilliant. 

Mrs.  B.  Certainly.  There  are  several  things  to 
be  observed  in  regard  to  the  form  and  extent  of  sha- 
dows. If  the  luminous  body  A  (fig.  3.)  is  larger  than 
the  opaque  body  B,  the  shadow  will  gradually  di- 
minish in  size,  till  it  terminate  in  a  point. 

Caroline.  This  is  the  case  with  the  shadows  of 
the  earth  and  the  moon,  as  the  sun  which  illumines 
them  is  larger  than  either  of  those  bodies.  And 
why  is  it  not  the  case  with  the  shadows  of  terrestrial 
objects,  which  are  equally  illumined  by  tffe  sun  ? 
but  their  shadows,  far  from  diminishing,  are  always 
larger  than  the  object,  and  increase  with  the  dis- 
tance from  it. 

Mrs.  B.  In  estimating  the  effect  of  shadows,  we 
must  consider  the  apparent  not  the  real  dimensions 
of  the  luminous  body  ;  and  in  this  point  of  view,  the 
sun  is  a  small  object  compared  with  the  generality  of 
the  terrestrial  bodies  which  it  illumines  :  and  when 
the  luminous  body  is  less  than  the  opaque  body,  the 
shadow  will  increase  with  the  distance  to  infinity. 
All  objects,  therefore,  which  are  apparently  larger 
than  the  sun,  cast  a  maccnified  shadow.  This  will 
17* 


198  ON  OPTICA. 

be  best  exemplified,  by  observing  the  shadow  oi  au 
object  lighted  by  a  candle. 

Emily.  I  have  often  noticed,  that  the  shadow  of 
my  figure  against  the  wall,  grows  larger  as  it  is  more 
distant  from  me,  which  is  owing,  no  doubt,  to  the  can- 
dle that  shines  on  me  being  much  smaller  than  my- 
self? 

Mrs.  B.  Yes.  The  shadow  of  a  figure  A,  (fig.  4,) 
varies  in  size,  according  to  the  distance  of  the  several 
surfaces  B  C  D  E,  on  which  it  is  described. 

Caroline.  1  have  observed,  that  two  candles  pro- 
duce two  shadows  from  the  same  object ;  whilst  it 
would  appear,  from  what  you  said,  that  they  should 
rather  produce  only  half  a  shadow,  that  is  to  say,  a 
very  faint  one. 

Mrs.  B.  The  number  of  lights  (in  different  direc- 
tions) while  it  decreases  the  intensity  of  the  sha- 
dow, increases  their  number,  which  always  corres- 
ponds with  that  of  the  lights  ;  for  each  light  makes 
the  opaque  body  cast  a  different  shadow,  as  illustrated 
by  figure  5.  It  represents  a  ball  A,  lighted  by  three 
candles  B,  C,  D,  and  you  observe  the  light  B  pro- 
duces the  shadow  6,  the  light  C  the  shadow  c,  and  the 
light  D  the  shadow  d. 

Emily.  I  think  we  now  understand  the  nature  of 
shadows  very  well  ;  but  pray  what  becomes  of  the 
rays  oi^ light  which  opaque  bodies  arrest  in  their 
course,  and  the  interruption  of  which  is  the  occasion 
of  shadows  ? 

Mrs.  B.  Your  question  leads  to  a  very  important 
property  of  light.  Reflection.  When  rays  of  light 
encounter  an  opaque  body,  which  they  cannot  tra- 
verse, part  of  them  are  absorbed  by  it,  and  part  are 
leflected,  and  rebound  just  as  an  elastic  ball  which  is 
struck  against  a  wall. 

Emily.  And  is  light  in  its  reflection  governed  by 
the  same  laws  as  solid  elastic  bodies  ? 

Mrs.  B.  Exactly.  If  a  ray  of  light  fall  perpendi- 
eularly  on  an  opaque  body,  it  is  reflected  back  in  the 
same  line,  towards  the  point  whence  it  proceeded. 


ON   OPTICSi  191* 

If  it  fall  obliquely,  it  is  reflected  obliquely,  but  in  the 
opposite  direction  ;  the  angle  of  incidence  being  equal 
to  the  angle  of  reflection.  You  recollect  that  law  in 
mechanics  ? 

Emily.     Oh  yes,  perfectly, 

Mrs.  B.  If  you  will  shut  the  shutters,  we  shall 
admit  a  ray  of  the  sun's  light  through  a  very  small 
aperture,  and  I  can  show  you  how  it  is  reflected,  i 
now  hold  this  mirror,  so  that  the  ray  shall  fall  per- 
pendicularly upon  it. 

Caroline.  I  see  the  ray  which  falls  upon  the  mir- 
ror, but  not  that  which  is  reflected  by  it. 

Mrs.  B.  Because  its  reflection  is  directly  retro- 
grade. The  ray  of  incidence  and  that  of  reflection 
both  being  in  ti»e  same  line,  though  in  opposite  direc- 
tions, are  confounded  together. 

Emily.  The  ray  then  which  appears  to  us  single, 
is  really  double,  and  is  composed  of  the  incident  ray 
proceeding  to  the  mirror,  and  of  the  reflected  ray  re- 
turning from  the  mirror. 

Mrs.  B.  Exactly  so.  We  shall  now  separate  them, 
by  holding  the  mirror  M,  (fig.  6,)  in  such  a  manner, 
that  the  incident  ray  A  B  shall  fall  obliquely  upon  it 
— you  see  the  reflected  ray  B  C,  is  marching  off"  in 
another  direction.  If  we  draw  a  line  from  the  point 
of  incidence  B,  perpendicular  to  the  mirror,  it  will 
divide  the  angle  of  incidence  from  the  angle  of  re- 
flection, and  you  will  see  that  they  are  equal. 

Emily.  Exactly  ;  and  now  that  you  hold  the  mir- 
ror so,  that  the  ray  falls  more  obliquely  on  it,  it  is 
also  reflected  more  obliquely,  preserving  the  equality 
of  the  angles  of  incidence  and  reflection. 

Mrs.  B.  It  is  by  reflected  rays  only  that  we  see 
opaque  objects.  Luminous  bodies  send  rays  of  light 
immediately  to  our  eyes,  but  the  rays  which  they 
send  to  other  bodies  are  invisible  to  us,  and  are  seen 
only  when  they  are  reflected  or  transmitted  by  those 
bodies  to  our  eyes. 

Emily.  But  have  we  not  just  seen  the  ray  of  light 
in  its  passage  from  the  sua  to  the  mirror^  and  its  re- 


200  ON    OPTICS. 

flection  ?  yet  in  neither  case  were  those  rays  in  a  di- 
rection to  enter  our  eyes. 

Mrs.  B.  No.  What  you  saw  was  the  light  reflect- 
ed to  your  eyes  by  small  particles  of  dust  floating  in 
the  air,  and  on  which  the  ray  shone  in  its  passage  to 
and  from  the  mirror. 

Caroline.  Yet  I  see  the  sun  shining  on  that  house 
yonder,  as  clearly  as  possible. 

Mrs.  B.  Indeed  you  cannot  sec  a  single  ray  which 
passes  from  the  sun  to  the  house  ;  you  see  no  rays 
but  those  whicli  enter  your  eyes  ;  therefore  it  is  the 
rays  which  are  reflected  by  the  house  to  you,  and  not 
those  which  proceed  from  tlie  sun  to  the  house,  that 
are  visible  to  you. 

Caroline.  Why  then  does  one  side  of  the  house 
appear  to  be  in  sunshine,  and  the  other  in  the  shade  ? 
for  if  I  cannot  see  the  sun  shine  upon  it,  the  whole  of 
the  house  should  appear  in  the  shade. 

Mrs.  B.  That  side  of  the  house  which  the  sun 
shines  upon,  reflects  more  vivid  and  luminous  rays 
than  the  side  which  is  in  shadow,  for  the  latter  is  illu- 
mined only  by  rays  reflected  upon  it  by  other  objects, 
these  rays  are  therefore  twice  reflected  before  they 
reach  your  sight  ;  and  as  light  is  more  or  less  absorb- 
ed by  the  bodies  it  strikes  upon,  every  time  a  ray  is 
reflected  its  intensity  is  diminished. 

Caroline.  Still  I  cannot  reconcile  myself  to  the 
idea,  that  we  do  not  see  the  sun's  rays  shining  on  ob- 
jects, but  only  those  which  objects  reflect  to  us. 

Mrs.  B.  I  do  not,  however,  despair  of  convincing 
you  of  it.  Look  at  that  large  sheet  of  water,  can  you 
tell  me  why  the  sun  appears  to  shine  on  one  part  of 
it  only  ? 

Caroline.  No,  indeed  ;  for  the  whole  of  it  is  equal- 
ly exposed  to  the  sun.  This  partial  brilliancy  of  wa- 
ter has  often  excited  my  wonder  ;  but  it  has  struck 
me  more  particularly  by  moonlight.  I  have  fre- 
quently observed  a  vivid  streak  of  moonshine  on  the 
sea,  while  the  rest  of  the  water  remained  in  deep 
obscurity,  and  yet  there  was  no  apparent  obstacle  to 


ON   OPTICS.  201 

prevent  the  moon  from  shining  on  every  part  of  the 
water  equally. 

Mrs.  B.  By  moonlight  the  effect  is  more  remark- 
able, on  account  of  the  deep  obscurity  of  the  other 
parts  of  the  water ;  while  by  the  sun's  light  the  ef- 
fect is  too  strong  for  the  eye  to  be  able  to  contem*- 
plate  it. 

Caroline,  But  if  the  sun  really  shines  on  every 
part  of  that  sheet  of  water,  why  does  not  every 
part  of  it  reflect  rays  to  my  eyes  ? 

Mrs.  B.  The  reflected  rays  are  not  attracted  out 
of  their  natural  course  by  your  eyes.  The  direction 
of  a  reflected  ray,  you  know,  depends  on  that  of  the 
incident  ray  ;  the  sun's  rays,  therefore,  which  fall 
with  various  degrees  of  obliquity  upon  the  water,  are 
reflected  in  directions  equally  various  ;  some  of  these 
will  meet  your  eyes,  and  you  will  see  them,  but  those 
which  fall  elsewhere  are  invisible  to  you. 

Caroline.  The  streak  of  sunshine,  then,  which 
we  now  see  upon  the  water,  is  composed  of  those 
rays  which  by  their  reflection  happen  to  fall  upon  my 
eyes  ? 

Mrs.  B.     Precisely. 

Emily.  But  is  that  side  of  the  house  yonder,  which 
appears  to  be  in  shadow,  really  illumined  by  the  sun, 
and  its  rays  reflected  another  way  ? 

Mrs.  B.  No  ;  that  is  a  diff'erent  case  from  the 
sheet  of  water.  That  side  of  the  house  is  really  in 
shadow  ;  it  is  the  west  side,  which  the  sun  cannot 
shine  upon  till  the  afternoon. 

Emily.  Those  objects,  then,  which  are  illumined 
by  reflected  rays,  and  those  which  receive  direct  rays 
from  the  sun,  but  which  do  not  reflect  those  rays  to- 
wards us,  appear  equally  in  shadow  ? 

Mrs.  B.  Certainly  ;  for  we  see  them  both  illu- 
mined by  reflected  rays.  That  part  of  the  sheet  of 
water,  over  which  the  trees  cast  a  shadow,  by  what 
light  do  you  see  it  ? 

Emily.     Since  it  is  not  by  the  sun's  direct  rays,  it 


202  ON  OPTICS. 

must  be  by  those  reflected  on  it  from  other  objects, 
and  which  it  again  reflects  to  us. 

Caroline.  But  if  we  see  all  terrestrial  objects  by 
reflected  light,  (as  we  do  the  moon,)  why  do  they  ap- 
pear so  bright  and  luminous  ?  1  should  have  suppos- 
ed that  reflected  rays  would  have  been  dull  and  faint, 
like  those  of  the  moon. 

Mrs.  B.  The  moon  reflects  the  sun's  light  with  as 
much  vividness  as  any  terrestrial  object.  If  you 
look  at  it  on  a  clear  night,  it  will  appear  as  bright  as 
a  sheet  of  water,  the  walls  of  a  house,  or  any  object 
seen  by  daylight,  and  on  which  the  sun  shines.  The 
rays  of  the  moon  are  doubtless  feeble,  when  compar- 
ed with  those  of  the  sun  ;  but  that  would  not  be  a 
fair  comparison,  for  the  former  are  incident,  the  lat- 
ter reflected  rays. 

Caroline.  True  ;  and  when  we  see  terrestrial  ob- 
jects by  moonlight,  the  light  has  been  twice  reflected, 
and  is  consequently  proportionally  fainter. 

Mrs.  B.  In  traversing  the  atmosphere,  the  rays, 
both  of  the  sun  and  moon,  lose  some  of  their  light.  ^ 
For  though  the  pure  air  is  a  transparent  medium, 
which  transmits  the  rays  of  light  freely,  we  have  ob- 
served, that  near  the  surface  of  the  earth  it  is  loaded 
with  vapours  and  exhalations,  by  which  some  portion 
of  them  are  absorbed. 

Caroline.  I  have  often  noticed,  that  an  object  oq 
the  summit  of  a  hill  appears  more  distinct  than  one 
at  an  equal  distance  in  a  valley,  or  on  a  plain  ;  which  is 
owing,  I  suppose,  to  the  air  being  more  free  from  va- 
pours in  an  elevated  situation,  and  the  reflected  rays 
being  consequently  brighter. 

Mrs.  B.  That  may  have  some  sensible  effect ;  but 
when  an  object  on  the  summit  of  a  hill  has  a  back 
ground  of  light  sky,  the  contrast  with  the  object 
makes  its  outline  more  distinct. 

Caroline.  I  now  feel  well  satisfied,  that  we  see 
opaque  objects  only  by  reflected  rays ;  but  I  do  not 
understand  how  these  rays  show  us  the  objects  from 
which  they  proceed  ? 


ON  OPTICS.  203 

Mrs,  B.  The  rays  of  li^ht  enter  at  the  pupil  of 
the  eye,  and  proceed  to  the  retina,  or  optic  nerve, 
which  is  situated  at  the  back  part  of  the  eye-ball ; 
and  there  they  describe  the  (isjure,  colour,  and  (ex- 
cepting size)  form  a  perfect  representation  of  the  ob- 
ject from  which  they  proceed.  We  shall  again  dose 
the  shutters,  and  admit  the  light  through  the  small 
aperture,  and  yo  ;  will  see  a  picture  on  the  wall,  op- 
posite the  ap«*rture,  similar  to  that  which  is  delinea- 
ted on  the  retina  of  the  eye. 

Caroline.  Oh,  how  wonderful!  There  is  an  exact 
picture  in  miniature  of  the  garden,  the  gardener  at 
work,  the  trees  blown  about  by  the  wind.  The 
landscape  would  be  perfect,  if  it  were  not  reversed ; 
the  ground  being  ab  )ve.  and  the  sky  beneath. 

Mrs.  B.  Is  it  not  enough  to  admire,  you  must  un- 
derstand this  phenomenon,  which  is  called  a  camera 
obscura,  from  the  necessity  of  darkening  the  room,  in 
order  to  exhibit  it. 

This  picture  is  produced  by  the  rays  of  light  re- 
flected from  the  various  objects  in  the  garden,  and 
which  are  admitted  through  the  hole  in  the  window- 
shutter. 

The  rays  from  the  glittering  weathercock  at  the 
top  of  the  alcove  A,  (Plate  XVI.  fig.  1.)  represent  it  in 
this  spot  a;  for  the  weathercock  being  much  higher 
than  the  aperture  in  the  shutter,  only  a  few  of  the 
rays,  which  are  reflected  by  it  in  an  obliquely  de- 
scending direction,  can  find  entrance  there.  The 
rays  of  light,  you  know,  always  move  in  straight 
lines ;  those,  therefore,  which  enter  the  room  in  a 
descending  direction,  will  continue  their  course  in 
the  same  direction,  and  will,  consequently,  fall  upon 
the  lower  part  of  the  wall  opposite  the  aperture,  and 
represent  the  weathercock  reversed  in  that  spot,  in- 
stead of  erect  in  the  uppermost  part  of  the  landscape. 
Emily.  And  the  rays  of  light  from  the  steps  (B) 
of  the  alcove,  in  entering  the  aperture,  ascend,  and 
will  describe  those  steps  in  the  highest  instead  of  the 
lowest  part  of  the  landscape. 


204  ©N  OPTICS. 

Mrs.  B.  Observe,  too,  that  the  rays  coming  from 
the  alcove,  which  is  to  our  left,  describe  it  on  the 
wall  to  the  right ;  while  those  which  are  reflected  by 
the  walnut-tree  C  D,  to  our  right,  delineate  its  figure 
in  the  picture  to  the  left,  c  d.  Thus  the  rays,  cona- 
ing  in  different  directions,  and  proceeding  always  in 
right  lines,  cross  each  other  at  their  entrance  through 
the  aperture:  those  which  come  above  proceed  be- 
low, those  from  the  right  go  to  the  left,  those  from 
the  left  towards  the  right ;  thus  every  object  is  re- 
presented in  tlie  picture,  as  occupying  a  situation  the 
very  reverse  of  that  which  it  does  m  nature. 

Caroline.  Excepting  the  flower-pot  E  F,  which, 
though  its  position  is  reversed,  has  not  changed  its 
situation  in  the  landscape. 

Mrs.  B.  The  flower-pot  is  directly  in  front  of  the 
aperture ;  so  that  its  rays  fall  perpendicularly  upon 
it,  and,  consequently,  proceed  perpendicularly  to  the 
wall,  where  they  delineate  the  object  directly  behind 
the  aperture. 

Emily.  And  is  it  thus  that  the  picture  of  objects  is 
painted  on  the  retina  of  the  eye  ? 

Mrs.  B.  Precisely.  The  pupil  of  the  eye, 
through  wliich  the  rays  of  light  enter,  represents  the 
aperture  in  the  window-shutter  ;  and  the  image  deli-r 
neated  on  the  retina,  is  exactly  similar  to  the  picture 
on  the  wall. 

Caroline.  You  do  not  mean  to  say,  that  we  see  only 
the  representation  of  the  object  which  is  painted  oq 
the  retina,  and  not  the  object  itself? 

Mrs.  B.  If,  by  sight,  you  understand  that  sense 
by  which  the  presence  of  objects  is  perceived  by  the 
mind,  through  the  means  of  the  eyes,  we  certainly 
see  only  the  image  of  those  objects  painted  on  the 
retina. 

Caroline.     This  appears  to  me  quite  incredible. 

Mrs.  B.  The  nerves  are  the  only  part  of  our 
frame  capable  of  sensation :  they  appear,  therefore^ 
to  be  the  instruments  which  the  mind  employs  in  its 
perceptions  :  for  a  sensation  always  conveys  an  idea 


J'LATE.   JCVI. 


/h 

A 

/         ^      H         \ 

\ 

ON  OPTICS.  205 

to  the  mind.  Now  it  is  known,  that  our  nerves  can 
be  affected  only  by  contact ;  and  for  this  reason  the 
organs  of  sense  cannot  act  at  a  distance  :  for  instance, 
we  are  capable  of  smelling  only  particles  which  are 
actually  in  contact  with  the  nerves  of  the  nose.  We 
have  already  observed,  that  the  odour  of  a  flower 
consists  in  etfluvia,  composed  of  very  minute  particles, 
which  penetrate  the  nostrils,  and  strike  upon  the  ol- 
factory nerves,  which  instantly  convey  the  idea  of 
smell  to  the  mind. 

Emily.  And  sound,  though  it  is  said  to  be  heard  at 
a  distance,  is,  in  fact,  heard  only  when  the  vibrations 
of  the  air,  which  convey  it  to  our  ears,  strike  upon 
the  auditory  nerve. 

Caroline.  There  is  no  explanation  required,  to 
prove  that  the  senses  of  feeling  and  of  tasting  are  ex- 
cited only  by  contact. 

Mrs.  B.  And  I  hope  to  convince  you,  that  the 
sense  of  sight  is  so  likewise.  The  nerves,  which 
constitute  the  sense  of  sight,  are  not  different  in  their 
nature  from  those  of  the  other  organs  ;  they  are 
merely  instruments  which  convey  ideas  to  the  mind, 
and  can  be  affected  only  on  contact.  Now,  since  real 
objects  cannot  be  brought  to  touch  the  optic  nerve, 
the  image  of  them  is  conveyed  thither  by  the  rays  of 
light  proceeding  from  real  objects,  which  actually 
strike  upon  the  optic  nerve,  and  form  that  image  which 
the  mind  perceives. 

Caroline.  While  I  listen  to  your  reasoning,  I  feel 
convinced  ;  but  when  I  look  upon  the  objects  around, 
and  think  that  I  do  not  see  them,  but  merely  their 
image  painted  in  my  eyes,  my  belief  is  again  stagger- 
ed. I  cannot  reconcile  myself  to  the  idea,  that  1  do 
not  really  see  this  book  which  I  hold  in  my  hand,  nor 
the  words  which  I  read  in  it. 

Mrs.  B.  Did  it  ever  occur  to  you  as  extraordina- 
ry, that  you  never  beheld  your  own  face  ? 

Caroline.  No  ;  because  I  so  frequently  see  an  ex- 
act representation  of  it  in  the  looking-glass. 

v¥r<?.  B.    You  see  a  far  more  exact  representation 
18 


206  ox  OPTICS. 

©f  objects  on  the  retina  of  your  eye  :  it  is   a  much 
more  perfect  mirror  than  any  made  by  art. 

Emily.  But  is  it  possible,  that  the  extensive  land- 
scape, which  I  now  behold  from  the  window,  should 
be  represented  on  so  small  a  space  as  the  retina  of 
the  eye  ? 

Mrs.  B.  It  would  be  impossible  for  art  to  paint  so 
small  and  distinct  a  miniature  ;  but  nature  works  with 
a  surer  hand,  and  a  more  delicate  pencil.  That  pow- 
er, which  forms  the  feathers  of  the  butterfly,  and  the 
flowerets  of  the  daisy,  can  alone  portray  so  admira- 
ble and  perfect  a  miniature  as  that  which  is  represent- 
ed on  the  retina  of  the  eye. 

Caroline,  But,  Mrs.  B.,  if  we  see  only  the  image 
of  objects,  why  do  we  not  see  them  reversed,  as  you 
showed  us  they  were  in  the  camera  obscura  ?  Is  not 
that  a  strong  argument  against  your  theory  ? 

Mrs,  B.  Not  an  unanswerable  one,  I  hope.  The  im- 
age on  the  retina,  it  is  true,  is  reversed,  like  that  in  the 
camera  obscura ;  as  the  rays,  unless  from  a  very  small 
object,  intersect  each  other  on  entering  the  pupil  in 
the  same  manner  as  they  do  on  entering  the  camera 
obscura.  The  scene,  however,  does  not  excite  the 
idea  of  being  inverted,  because  we  always  see  an  ob- 
ject in  the  direction  of  the  rays  which  it  sends  to  us. 

Emily.     I  confess  I  do  not  understand  that. 

Mrs.  B.  It  is,  r  think,  a  diflicult  point  to  explain 
clearly.  A  ray  which  comes  from  the  upper  part  of 
an  object,  describes  the  image  on  the  lower  part  of 
the  retina  ;  but  experience  having  taught  us,  that  the 
direction  of  that  ray  is  from  above,  we  consider  that 
part  of  the  object  it  represents  as  uppermost.  The 
rays  proceeding  from  the  lower  part  of  an  object  fall 
upon  the  upper  part  of  the  retina;  but  as  we  know  their 
direction  to  be  from  below,  we  see  that  part  of  the  ob- 
ject they  describe  as  the  lowest. 

Caroline.  When  1  want  to  see  an  object  above  me, 
I  look  up  ;  when  an  object  below  me,  I  look  down. 
Does  not  this  prove  that  I  see  the  objects  themselves? 
for  if  I  beheld  only  the  image,  there  would  be  no 


osr  OPTICS'.  207 

necessity  for  looking  up  or  down,  according  as  the 
©bject  was  higher  or  lower  than  myself. 

Mrs.  B.  I  beg  your  pardon.  When  you  look  up  to 
an  elevated  object,  it  is  in  order  that  the  rays  reflect- 
ed froKi  it  should  fall  upon  the  retina  of  your  eyes  ; 
but  the  very  circumstance  of  directing  you  eyes  up- 
wards convinces  you  that  the  object  is  elevated,  and 
teaches  you  to  consider  as  uppermost  the  image  it 
forms  on  the  retina,  though  it  is,  in  fact,  represented 
in  the  lowest  part  of  it.  When  you  look  down  up- 
on an  object,  you  draw  3'^our  conclusion  from  a  simi- 
lar reasoning  ;  it  is  thus  that  we  see  all  objects  in  the 
direction  of  the  rays  which  reach  our  eyes. 

But  I  have  a  further  proof  in  favour  of  what  I 
have  advanced,  which,  I  hope,  will  remove  your  re- 
maining doubts  ;  I  shall,  hovvever,  defer  it  till  our 
next  meeting,  as  the  lesson  has  been  sulBciently  long'. 
to-day. 


CONVERSATION  XV. 


OTTlCS^continued. 

ON  THE  ANGLE  OF  VISION,   AND   THE 
REFLECTION  OF  MIRRORS. 

Angle  of  Vision. — Reflection  of  Plain  Mirrors. •-' Re- 
flection of  Convex  Mirrors. — Reflection  of  Concave 
Mirrors. 

CAROLINE.  Well,  Mrs.  B.,  I  am  very  impatient 
to  hear  what  further  proofs  you  have  to  offer  in  sup- 
port of  your  theory.  You  must  allow  that  it  was 
rather  provoking  to  dismiss  us  as  you  did  at  our  last 
meeting. 

Mrs.  B.  You  press  so  hard  upon  me  with  your 
objections,  that  you  must  give  me  time  to  recruit  my 
forces. 

Can  you  tell  me,  Caroline,  why  objects  at  a  dis- 
tance appear  smaller  than  they  really  are  ? 

Caroline.  I  know  no  other  reason  than  their  dis- 
tance. 

Mrs.  B.  I  do  not  think  I  have  more  cause  to  be 
satisfied  with  your  reasons  than  you  appear  to  be 
with  mine.  We  must  refer  again  to  the  camera  ob- 
scura  to  account  for  this  circumstance  ;  and  3'ou  will 
iind,  that  the  different  apparent  dimensions  of  objects 
at  different  distances,  proceed  from  our  seeing,  not 
the  objects  themselves,  but  merely  their  image  on 
the  retina.     Fig.  1.  Plate  XVII.  represents  a  row  of 


PLATE.  XV, 


ON  THE  ANGLE  OF  VISION.  209 

trees,  as  viewed  in  the  camera  obscura.  I  have  ex- 
pressed the  direction  of  the  rays,  from  the  objects  to 
the  image,  by  lines.  Now,  observe,  the  ray  which 
comes  from  the  top  of  the  nearest  tree,  and  that 
which  comes  from  the  foot  of  the  same  tree,  meet  at 
the  aperture,  forming  an  angle  of  about  twenty-five 
degrees  ;  this  is  called  the  angle  of  vision,  under 
which  we  see  the  tree.  These  rays  cross  each 
other  at  the  aperture,  forming  equal  angles  on  each 
side'of  it,  and  represent  the  tree  inverted  in  the  ca- 
mera obscura.  The  degrees  of  the  image  are  consi- 
derably smaller  than  those  of  the  object,  but  the  pro- 
portions are  perfectly  preserved. 

Now  let  us  notice  the  upper  and  lower  ray,  from 
the  most  distant  tree  ;  they  form  an  angle  of  not  more 
than  twelve  or  fifteen  degrees,  and  an  image  of  pro- 
portional dimensions.  Thus,  two  objects  of  the  same 
size,  as  the  two  trees  of  the  avenue,  form  figures  of 
different  sizes  in  the  camera  obscura,  according  to 
their  distance  ;  or,  in  other  words,  according  to  the 
angle  of  vision  under  which  they  are  seen.  Do  yoa 
understand  this  ? 

Caroline.     Perfectly. 

Mrs.  B.  Then  you  have  only  to  sappose  that  the 
representation  in  the  camera  obscura  is  similar  to  that 
on  the  retina. 

Now  since  objects  of  the  same  magnitudes  appear 
to  be  of  different  dimensions,  when  at  different  distan- 
ces from  us,  let  me  ask  you,  which  it  is  that  we  see  j 
the  real  objects,  which  we  know  do  not  vary  in  size, 
or  the  images,  which  we  know  do  vary  according  to 
the  angle  of  vision  under  which  we  see  them  ? 

Caroline.  I  must  confess,  that  reason  is  in  favour 
of  the  latter.  But  does  that  chair  at  the  further  end 
of  the  room  form  an  image  on  my  retina  much  smaller 
than  this  which  is  close  to  me  ?  they  appear  exactly 
of  the  same  size. 

Mrs.  B.  1  assure  you  they  do  not.  The  expe- 
rience we  acquire  by  the  sense  of  touch  corrects  the 
errors  of  our  sight  with  regard  to  objects  withiu  our 
18* 


210  ON  THE  ANGLE  OF  VISIOTC. 

reacli.  You  are  so  perfectl}?  convinced  of  the  real 
size  of  objects  which  }'ou  can  handle,  that  3'ou  do  not 
attend  to  their  apparent  difference. 

Does  that  house  appear  to  you  much  smaller  than 
when  you  are  close  to  it  ^ 

Caroline,     No,  because  it  is  very  near  us. 

Mrs.  B.  And  yet  you  can  see  the  whole  of  it 
through  one  of  the  windows  of  this  room.  The 
image  of  the  house  on  your  retina  must,  therefore, 
be  smaller  than  that  of  the  window  through  which 
you  see  it.  It  is  your  knowledge  of  the  real  size  of 
the  house  which  prevents  your  attending  to  its  appa- 
rent magnitude.  If  you  were  accustomed  to  draw 
from  nature,  you  would  be  fully  aware  of  this  differ- 
ence.      ^ 

Emily.  And  pray,  what  is  the  reason  that,  when 
we  look  up  an  avenue,  the  trees  not  only  appear 
smaller  as  they  are  more  distant,  but  seem  gradually 
to  approach  each  other  till  they  meet  in  a  point? 

Mrs.  B.  Not  only  the  trees,  but  the  roiid  which 
separates  the  two  rows,  forms  a  smaller  visual  angle, 
in  proportion  as  it  is  more  distant  from  us  ;  there- 
fore the  width  of  the  road  gradually  diminishes  as 
well  as  the  size  of  the  trees,  till  at  length  the  road 
apparently  terminates  in  a  point,  at  which  the  trees 
seem  to  meet. 

But  this  effect  of  the  angle  of  vision  will  be  more 
fully  illustrated  by  a  little  model  of  an  avenue,  which 
I  have  made  for  that  purpose.  It  consists  of  six 
trees,  leading  to  a  hexagonal  temple,  and  viewed  by 
an  eye,  on  the  retina  of  which  the  picture  of  the 
objects  is  delineated. 

I  beg  that  you  will  not  criticise  the  proportions ; 
for  though  the  eye  is  represented  the  size  of  life, 
while  the  trees  are  not  more  than  three  inches  high, 
the  disproportion  does  not  affect  the  principle  which 
the  model  is  intended  to  elucidate. 

Emily.  The  threads  which  pass  from  the  objects 
through  the  pupil  of  the  eye  to  the  retina,  are,  I  sup- 


ON  TH£  ANGLE  OF  VISI©.\.  211 

pese,  to  represent  the  rays  of  light  which  convey  the 
image  of  the  objects  to  the  retina  ? 

Mrs.  B.  Yes.  i  have  been  obhged  to  limit  the 
rays  to  a  very  small  number,  in  order  to  avoid  confu- 
sion ;  there  are,  you  see,  only  two  from  each  tree. 

Caroline.  But  as  one  is  from  the  summit,  and  the 
other  from  the  foot  of  the  tree,  they  exemplify  the 
different  angles  under  which  we  see  objects  at  differ- 
ent distances,  better  than  if  there  were  more. 

Airs.  B.  There  are  seven  rays  proceeding  from 
the  temple,  one  from  the  summit,  and  two  from  each 
of  the  angles  that  are  visible  to  the  eye,  as  it  is  situ- 
ated ;  from  these  you  may  form  a  just  idea  of  the 
difference  of  the  angle  of  vision  of  objects  viewed 
obliquely,  or  in  front ;  for  though  the  six  sides  of  the 
temple  are  of  equal  dimensions,  that  which  is  oppo- 
eite  to  the  eye  is  seen  under  a  much  larger  angle 
than  those  which  are  viewed  obliquely.  It  is  on  this 
principle  that  the  laws  of  perspective  are  founded. 

Emily.  I  am  very  glad  to  know  that,  for  I  have 
lately  begun  to  learn  perspective,  which  appeared  to 
me  a  very  dry  study  ;  but  now  that  1  am  acquainted 
with  the  principles  on  which  it  is  founded,  I  shall 
find  it  much  more  interesting. 

Caroline.  In  drawing  a  view  from  nature,  then, 
we  do  not  copy  the  real  objects,  but  the  image  they 
form  on  the  retina  of  our  eyes  ? 

Mrs.  B.  Certainly.  In  sculpture,  we  copy  nature 
as  she  really  exists ;  in  painting,  we  represent  her  as 
she  appears  to  us.  It  was  on  this  account  that  1  found 
it  difficult  to  explain,  by  a  drawing,  the  effects  of  the 
angle  of  vision,  and  was  under  the  necessity  of  con- 
structing a  model  for  that  purpose. 

Emily.  1  hope  you  will  allow  us  to  keep  this  mo- 
del some  time,  in  order  to  study  it  more  completely, 
for  a  great  deal  may  be  learned  from  it;  it  illustrates 
the  nature  of  the  angle  of  vision,  the  apparent  dimi- 
nution of  distant  objects,  and  the  inversion  of  the 
image  on  the  retina.    But  pray,  why  are  the  threads. 


212  ON  THE  ANGLE  OF  VISION. 

that  represent  the  rays  of  light  coloured,  the  same  as 
the  objects  from  which  they  proceed  ? 

Mrs.  B.  That  is  a  question  which  you  must  excuse 
my  answering  at  present,  but  I  promise  to  explain  it 
to  you  in  due  time. 

I  consent  very  willingly  to  your  keeping  the  model, 
on  condition  that  you  will  make  an  imitation  of  it,  on 
the  same  principle,  but  representing  different  objects. 

We  must  now  conclude  the  observations  that  re- 
main to  be  made  on  the  angle  of  vision. 

If  an  object,  with  an  ordinary  degree  of  illumina- 
tion, does  not  subtend  an  angle  of  more  than  two  se- 
conds of  a  degree,  it  is  invisible.  There  are  conse- 
quently two  cases  in  which  objects  may  be  invisible, 
either  if  they  are  too  small,  or  so  distant  as  to  form 
an  angle  less  than  two  seconds  of  a  degree. 

In  like  manner,  if  the  velocity  of  a  body  does  not 
exceed  20  degrees  in  an  hour,  its  motion  is  impercep- 
tible. 

Caroline.  A  very  rapid  motion  may  then  be  im- 
perceptible, provided  the  distance  of  the  moving  body 
is  sufficiently  great. 

Mrs.  B.  Undoubtedly  ;  for  the  greater  its  distance, 
the  smaller  will  be  the  angle  under  which  its  motion 
will  appear  to  the  eye.  It  is  for  this  reason  that  the 
motion  of  the  celestial  bodies  is  invisible,  notwith- 
standing their  immense  velocity.  -* 

Emily.  I  am  surprised  that  so  great  a  velocity  as 
20  degrees  an  hour  should  be  invisible. 

Mrs.  B.  The  real  velocity  depends  altogether  on 
the  space  comprehended  in  each  degree  ;  and  this 
space  depends  on  the  distance  of  the  object,  and  the 
obliquity  of  its  path.  Observe,  likewise,  that  we 
cannot  judge  of  the  velocity  of  a  body  in  motion  un- 
less we  know  its  distance  ;  for  supposing  two  men  to 
set  off  at  the  same  moment  from  A  and  B,  (tig.  2.)  to 
walk  each  to  the  end  of  their  respective  lines  C  and 
D;  if  they  perform  their  walk  in  the  same  space  of 
time,  they  must  have  proceeded  at  a  very  different 
rate,  aad  yet  to  an  eye  situated  at  £,  they  will  ap> 


ON  THE  ANGLE  OF  VISION.  "213 

pear  to  have  moved  with  equal  velocity :  because 
they  will  both  have  gone  through  an  equal  number 
of  degrees,  though  over  a  very  unequal  length  of 
ground.  Sight  is  an  cxtremel}^  useful  sense  no  doubt, 
but  it  cannot  always  be  relied  on,  it  deceives  us  both 
in  regard  to  the  size  and  the  distance  of  objects  ;  in- 
deed our  senses  would  be  very  liable  to  lead  us  into 
error,  if  experience  did  not  set  us  right. 

Emily.  Between  the  two,  I  think  that  we  contrive 
to  acquire  a  tolerably  accurate  idea  of  objects. 

Mrs.  B.  At  least  sufliciently  so  for  the  general 
purposes  of  life.  To  convince  you  how  requisite 
experience  is  to  correct  the  errors  of  sight,  1  shall 
relate  to  you  the  case  of  a  young  man  who  was  blind 
from  his  infancy,  and  who  recovered  his  sight  at  the 
age  of  fourteen,  by  the  operation  of  couching.  At 
first,  he  had  no  idea  either  of  the  size  or  distance  of 
objects,  but  imagined  that  every  thing  he  saw  tough- 
ed his  eyes  ;  and  it  was  not  till  after  having  repeated- 
ly felt  them,  and  walked  from  one  object  to  another» 
that  he  acquired  an  idea  of  their  respective  dimen- 
sions, their  relative  situations,  and  their  distances. 

Carolina/,  The  idea  that  objects  touched  his  eyeS 
is,  however,  not  so  absurd  as  it  at  first  appears  ;  for 
if  we  consider  that  we  see  only  the  image  of  objects, 
this  image  actually  touches  our  eyes. 

Mrs.  B.  That  is  doubtless  the  reason  of  the  opi- 
nion he  formed,  before  the  sense  of  touch  had  cor- 
rected his  judgment. 

Caroline.  But  since  an  image  must  be  formed  on 
the  retina  of  each  of  our  eyes,  why  do  we  not  see 
objects  double  ? 

Mrs.  B.  The  action  of  the  rays  on  the  optic 
nerve  of  each  eye  is  so  perfectly  similar,  that  they 
produce  but  a  single  sensation,  the  mind  therefore 
receives  the  same  idea,  from  the  retina  of  both  eyes, 
and  conceives  the  object  to  be  single. 

Caroline.  This  is  difficult  to  comprehend,  and,  I 
should  think,  can  be  but  conjectural. 

Mrs.  B.     I  can  easily  convince  you,  that  you  have 


214  ON    THE  ANGLE  er  VISION. 

a  distinct  image  of  an  object  formed  on  the  retina  of 
each  eye.  Look  at  the  bell-rope,  and  tell  me,  do  you 
see  it  to  the  right  or  the  left  of  the  pole  of  the  fire- 
skreen  ? 

Caroline.     A  little  to  the  right  of  it. 

Mrs.  B.  Then  shut  your  right  eye,  and  you  will 
see  it  to  the  left  of  the  pole. 

Caroline.     That  is  true  indeed  ! 

Mrs.  B.  There  are  evidently  two  representations 
of  the  bell-rope  in  different  situations,  which  must  be 
owing  to  an  image  of  it  being  formed  on  both  eyes  ;  if 
the  action  of  the  rays  therefore  on  each  retina  were 
not  so  perfectly  similar  as  to  produce  but  one  sensa- 
tion, we  should  see  double,  and  we  tind  that  to  be  the 
case  with  many  persons  who  are  afflicted  with  a  dis- 
ease in  one  eye,  which  prevents  the  rays  of  light 
from  affecting  it  in  the  same  manner  as  the  other. 

Emily'  Pray,  JMrs.  B.,  when  we  see  the  image  of 
an  object  in  a  looking-glass,  why  is  it  not  inverted  as 
in  the  camera  obscura,  and  on  the  retina  of  the  eye  ? 

Mrs.  B.  Because  the  rays  do  not  enter  the  mirror 
by  a  small  aperture,  and  cross  each  other,  as  they  do 
at  the  orifice  of  a  camera  obscura,  or  the  pupil  of  the 
eye. 

When  you  view  yourself  in  a  mirror,  the  rayS 
from  your  eyes  fall  perpendicularly  upon  it,  and  are 
reflected  in  the  same  line  ;  the  image  is  therefore 
described  behind  the  glass,  and  is  situated  in  the 
same  manner  as  the  object  before  it. 

Emily.  Yes,  I  see  tiiat  it  is  ;  but  the  looking-glass 
is  not  nearly  so  tall  as  I  am,  how  is  it  therefore  that 
I  can  see  the  whole  of  my  figure  in  it  ? 

Mrs.  B.  It  is  not  necessary  that  the  mirror  should 
be  more  than  half  your  height,  in  order  that  you  may 
8ee  the  whole  of  your  person  in  it,  (fig.  3.)  The 
ray  of  light  C  D  from  your  eye,  which  falls  perpen- 
dicularly on  the  mirror  B  D,  will  be  reflected  back 
in  the  same  line  ;  but  the  ray  from  your  feet  will 
fall  obliquely  on  the  mirror,  for  it  must  ascend  in  or- 
der to  reach  it  j  it  will  therefore  be  reflected  in  the 


ON   THE  ANGLE  GF  VISION.    .  21i5 

line  D  A  :  and  since  we  view  objects  in  the  direc- 
tion of  the  reflected  rays,  which  reach  the  eye,  and 
that  the  image  appears  at  the  same  distance  behind 
the  mirror  that  the  object  is  before  it,  we  must  con- 
tinue the  line  A  D  to  E,  and  the  line  C  D  to  F,  at  the 
termination  of  which  the  image  will  be  represented. 

Emily.  Then  I  do  not  understand  why  I  should 
not  see  the  whole  of  my  person  in  a  much  smaller 
mirror,  for  a  ray  of  light  from  my  feet  would  always 
reach  it,  though  more  obliquely. 

Mrs,  B.  True  ;  but  the  more  obliquely  the  ray 
falls  on  the  mirror,  the  more  obliquely  it  will  be  re- 
flected ;  the  ray  would  therefore  be  reflected  above 
your  head,  and  yon  could  not  see  it.  This  is  shown 
by  the  dotted  line  (fig.  3.) 

Now  stand  a  little  to  the  right  of  the  mirror,  so 
that  the  rays  of  light  from  your  figure  may  fall  ob- 
liquely on  it 

Emily.  There  is  no  image  formed  of  me  in  the 
glass  now. 

Mrs.  B.  I  beg  your  pardon,  there  is  ;  but  you 
cannot  see  it,  because  the  incident  rays  falling  ob- 
liquely on  the  mirror  will  be  reflected  obliquely  in 
the  opposite  direction,  the  angles  of  incidence  and  of 
reflection  being  equal.  Caroline,  place  yourself  in 
the  direction  of  the  reflected  rays,  and  tell  me  whe- 
ther you  do  not  see  Emily's  image  in  the  glass  ? 

Caroline.  Let  me  consider. — In  order  to  look  v». 
the  direction  of  the  reflected  rays,  I  must  place  n^^  ' 
self  as  much  to  the  left  of  the  glass  as  Emily  stanusto 
the  right  of  it. — Now  1  see  her  image,  but  it  is  not 
straight  before  me,  but  before  her  ;  and  appears  at 
the  same  distance  behind  the  glass,  as  she  is  in  front 
of  it. 

Mrs.  B.  You  must  recollect,  that  we  always  see 
objects  in  the  direction  of  the  last  rays  which  reach 
our  eyes.  Figure  4.  represents  an  eye  looking  at  the 
image  of  a  vase,  reflected  by  a  mirror  ;  it  must  see  it 
in  the  direction  of  the  ray  A  B,  as  that  is  the  raj" 


216  ON  THE  ANGLE  OF  VISION. 

which  brings  the  image  to  the  eye  ;  prolong  the  ray 
to  C,  and  in  that  spot  will  the  image  appear. 

Caroline,  I  do  not  understand  why  a  looking-glass 
reflects  the  rays  of  light  ;  for  glass  is  a  transparent 
body,  which  should  transmit  them  ? 

J\irs.  B.  It  is  not  the  glass  that  reflects  the  rays 
which  form  the  image  you  behold,  but  the  mercury 
behind  it.  The  glass  acts  chiefly  as  a  transparent 
case,  through  which  the  rays  find  an  easy  passage. 

Caroline,  Why  then  should  not  mirrors  be  made 
simply  of  mercury  ? 

Mrs.  B,  Because  mercury  is  a  fluid.  By  amal- 
gamating it  with  tin-foil,  it  becomes  of  the  consistence 
of  paste,  attaches  itself  to  the  glass,  and  forms  in  fact  a 
mercurial  mirror,  which  would  be  much  more  perfect 
without  its  glass  cover,  for  the  purest  glass  is  never 
perfectly  transparent :  some  of  the  rays  therefore  are 
lost  during  their  passage  through  it,  by  being  either 
absorbed,  or  irregularly  reflected. 

This  imperfection  of  glass  mirrors  has  introduced 
the  use  of  metallic  mirrors,  for  optical  purposes. 

Emily.  But  since  all  opaque  bodies  reflect  the 
rays  of  light,  I  do  not  understand  why  they  are  not 
all  mirrors  ? 

Caroline.  A  curious  idea  indeed,  sister  ;  it  would 
be  very  gratifying.to  see  one's  self  in  every  object  at 
which  one  looked. 

Mrs.  B,  It  is  very  true  that  all  opaque  objects  re- 
S*\^t  light  ;  but  the  surface  of  bodies  in  general  is  so 
rough  and  uneven,  that  their  reflection  is  extremely 
irregular,  which  prevents  the  rays  from  forming  an 
image  on  the  retina.  This  you  will  be  able  to  under- 
"stand  better,  when  I  shall  explain  to  you  the  nature 
of  vision,  and  the  structure  of  the  eye. 

You  may  easily  conceive  the  variety  of  directions 
in  which  rays  would  be  reflected  by  a  nutmeg-grater, 
on  account  of  the  inequality  of  its  surface,  and  the 
number  of  holes  with  which  it  is  pierced.  All  solid 
bodies  resemble  the  nutmeg-grater  in  these  respects, 
more  or  less ;  and  it  is  only  those  which  are  suscep- 


PLATE,  xvnr. 


ON    THE  ANGLE  OF  VISION.  S"!  7 

tible  of  receiving  a  polish,  that  can  be  made  to  reflect 
the  rays  with  regularity.  As  hard  bodies  are  of  the 
closest  texture,  the  least  porous,  and  capable  of  taking 
the  highest  polish,  they  make  the  best  mirrors  ; 
none,  therefore,  are  so  well  calculated  for  this  pur- 
pose as  metals. 

Caroline.  But  the  property  of  regular  reflection 
is  not  confined  to  this  class  of  bodies  ;  for  1  have  of- 
ten seen  myself  in  a  highly  polished  mahogany  table. 

Mrs.  B.  Certainly  ;  but  as  that  substance  is  less 
durable,  and  its  reflection  less  perfect,  than  that  of 
metals,  1  believe  it  would  seldom  be  chosen  for  the 
purpose  of  a  mirror. 

There  are  three  kinds  of  mirrors  used  in  optics ; 
the  plain  or  flat,  which  are  the  common  mirrors  we 
have  just  mentioned ;  convex  mirrors  ;  and  concave 
mirrors.  The  reflection  of  the  two  latter  is  very  dif- 
ferent from  that  of  the  former.  The  plain  mirror, 
we  have  seen,  does  not  alter  the  direction  of  the  re- 
flected rays,  and  forms  an  image  behind  the  glass 
exactly  similar  to  the  object  before  it.  A  convex 
mirror  has  the  peculiar  property  of  making  the  re- 
flected rays  diverge,  by  which  means  it  diminishes 
the  image  ;  and  a  concave  mirror  makes  the  rays  con- 
verge, and,  under  certain  circumstances,  magnifies  the 
image. 

Eiriily.  We  have  a  convex  mirror  in  the  drawing 
room  which  forms  a  beautiful  miniature  picture  of 
the  objects  in  the  room  ;  and  I  have  often  amused 
myself  with  looking  at  my  magnified  face  in  a  concave 
mirror.  But  1  hope  you  will  explain  to  us  why  the 
one  enlarges,  while  the  other  diminishes  the  objects 
it  reflects. 

Airs.  B.  Let  us  begin  by  examining  the  reflection 
of  a  convex  mirror.  This  is  formed  of  a  portion  of 
the  exterior  surface  of  a  sphere.  When  several  pa- 
rallel rays  fall  upon  it,  that  ray  only  which,  if  pro- 
longed, would  pass  through  the  centre  or  axis  of  the 
mirror,  is  perpendicular  to  it.  In  order  to  avoid  con- 
fusion, 1  have,  in  fig.  1.  Plat6  XVUl.,  drawn  only 
19 


218  ON    THE  ANGLE  OF  VISION. 

three  parallel  lines,  A  B,  C  D,  E  F,  to  represent 
rays  falling  on  the  convex  mirror  M  N  ;  the  middle 
ray,  you  will  observe,  is  perpendicular  to  the  mirror, 
the  others  fall  on  it  obliquely. 

Caroline.  As  the  three  rays  are  parallel,  why  are 
they  not  all  perpendicular  to  the  mirror  ? 

Mrs.  B.  They  would  be  so  to  a  flat  mirror  ;  but 
as  this  is  spherical,  no  ray  can  fall  perpendicularly 
upon  it  which  is  not  directed  towards  the  centre  of 
the  sphere. 

Emily.  Just  as  a  weight  falls  perpendicularly  to 
the  earth  when  gravity  attracts  it  towards  the  centre. 

Mrs.  B.  In  order,  therefore,  that  rays  may  fldl 
perpendicularly  to  the  mirror  at  B  and  F,  the  rays 
must  be  in  the  direction  of  the  dotted  lines,  which, 
you  may  observe,  meet  at  the  centre  O  of  the 
sphere,  of  which  the  mirror  forms  a  portion. 

Now  can  you  tell  me  in  what  direction  the  three 
rays,  A  B,  C  D,  E  F,  will  be  reflected  ? 

Emily.  Yes,  I  think  so;  the  middle  ray  falling 
perpendicularly  on  the  mirror,  will  be  reflected  in 
the  same  line:  the  two  others  falling  obliquely,  will 
be  reflected  obliquely  to  G  H  ;  for  the  dotted  lines 
you  have  drawn  are  perpendiculars,  which  divide 
their  angles  of  incidence  and  reflection. 

Mrs.  B.  Extremely  well,  Emily  :  and  since  we 
see  objects  in  the  direction  of  the  reflected  ray,  we 
shall  see  the  image  at  L,  which  is  the  point  at  which 
the  reflected  rays,  if  continued  through  the  mirror, 
would  unite  and  form  an  image.  The  point  is  equally 
distant  from  the  surface  and  centre  of  the  sphere,  and 
is  called  the  imaginary  focus  of  the  mirror. 

Caroline.  Pray,  what  is  the  meaning  of  focus  ? 
Mrs.  B.  A  point  at  which  converging  rays  unite. 
And  it  is  in  this  case  called  an  imaginary  focus  ;  be- 
cause the  rays  do  not  really  unite  at  that  point,  but 
only  appear  to  do  so  :  for  the  rays  do  not  pass  through 
the  mirror,  since  they  are  reflected  by  it. 

Emily.  I  do  not  yet  understand  why  an  object  ap- 
pears smaller  when  viewed  in  a  convex  mirror. 


O-V    THE  ANGLE  OF  TISION.  219 

J\Irs.  B.  It  is  owing  to  the  divergence  of  the  re- 
flected rays.  You  Avdve  seen  that  a  convex  mirror 
converts,  by  reflection,  parallel  rays  into  divergent 
rays  ;  rays  that  fall  upon  the  mirror  divergent,  are 
rendered  still  more  so  by  reflection,  and  convergent 
rays  are  reflected  either  parallel,  or  less  convergent. 
If  then  an  object  be  placed  before  any  part  of  a  con- 
vex mirror,  as  the  vase  A  B,  fig.  2.  for  instance,  the 
two  rays  from  its  extremities,  falling  convergent  on 
the  mirror,  will  be  reflected  less  convergent,  and  will 
not  come  to  a  locus  till  they  arrive  at  C  ;  then  an  eye 
placed  in  the  direction  of  the  reflected  rays  will  see 
the  image  formed  in  (or  rather  behind)  the  mirror  at 
a  b. 

Caroline.  But  the  reflected  rays  do  not  appear  to 
me  to  converge  less  than  the  incident  rays.  I  should 
have  supposed  that,  on  the  contrary,  they  converged 
more,  since  they  meet  in  a  point  ? 

Mrs.  B.  They  would  unite  sooner  than  they  actu- 
ally do,  if  they  were  not  less  convergent  than  the  in- 
cident rays  :  for  observe,  that  if  the  incident  rays,  ia- 
Etead  of  being  reflected  by  the  mirror,  continued  their 
course  in  their  original  direction,  they  would  come 
to  a  focus  at  D,  which  is  considerably  nearer  to  the 
mirror  than  at  C  ;  the  image  is  therefore  seen  under 
a  smaller  angle  than  the  object ;  and  the  more  dis- 
tant the  latter  is  from  the  mirror,  the  less  is  the 
image  reflected  by  it. 

You  wiH  now  easily  understand  the  nature  of  the 
reflection  of  concave  mirrors.  These  are  formed  of 
a  portion  of  the  internal  surface  of  a  hollow  sphere, 
and  their  peculiar  property  is  to  converge  the  rays 
©flight. 

Can  you  discover,  Caroline,  in  what  direction  the 
three  parallel  rays,  A  B,  C  D,  EF,  which  fall  on  the 
concave  mirror  M  N,  (fig.  3.)  are  reflected  ? 

Caroline.  I  believe  I  can.  The  middle  ray  is 
sent  back  in  the  same  line,  as  it  is  in  the  direction  of 
the  axis  of  the  mirror  ;  and  the  two  others  will  be 
reflected  obliquely,  as  they  fall  obhquely  on  the  mir- 


^20  ON   THE  ANGLE  OF  VISION. 

ror.  I  must  now  draw  two  dotted  lines  perpendicu- 
lar to  their  points  of  incidence,  which  will  divide 
their  angles  of  incidence  and  reflection  ;  and  in  order 
that  those  angles  may  be  equal,  the  two  oblique  rays 
must  be  reflected  to  L,  where  they  will  unite  with  the 
middle  ray. 

Mrs,  B.  Very  well  explained.  Thus  you  see, 
that  when  any  number  of  parallel  rays  fall  on  a  con- 
cave mirror,  they  are  all  reflected  to  a  focus  :  for,  in 
proportion  as  the  rays  are  more  distant  from  the  axis 
af  the  mirror,  they  fall  more  obliquely  upon  it,  and 
are  more  obliquely  reflected ;  in  consequence  of 
which  they  come  to  a  focus  in  the  direction  of  the 
axis  of  the  mirror,  at  a  point  equally  distant  from  the 
centre  and  the  surface  of  the  sphere,  and  this  point  is 
not  an  imaginary  focus,  as  happens  with  the  convex 
mirror,  but  is  the  true  focus  at  which  the  rays  unite. 

Emily.  Can  a  mirror  form  more  than  one  focus  by 
reflecting  rays  ? 

Mrs.  B.  Yes.  If  rays  fall  convergent  on  a  con- 
cave mirror,  (fig.  4.)  they  are  sooner  brought  to  a 
focus,  L,  than  parallel  rays  ;  their  focus  is  therefore 
nearer  to  the  mirror  M  N.  Divergent  rays  are 
brought  to  a  more  distant  focus  than  parallel  rays,  as 
in  figure  5,  where  the  focus  is  at  L  ;  but  the  true  fo- 
cus of  mirrors,  either  convex  or  concave,  is  that  of 
parallel  rays,  which  is  equally  distant  from  the  cen- 
tre, and  the  surface  of  the  sphere. 

I  shall  now  show  you  the  reflection  of  real  rays  of 
light,  by  a  metallic  concave  mirror.  This  is  one 
made  of  polished  tin,  which  I  expose  to  the  sun,  and 
fts  it  shines  bright,  we  shall  be  able  to  collect  the  rays 
into  a  very  brilliant  focus.  I  hold  a  piece  of  paper 
where  1  imagine  the  focus  to  be  situated  ;  you  may 
see  by  the  vivid  spot  of  light  on  the  paper,  how  much 
the  rays  converge  :  but  it  is  not  yet  exactly  in  the 
focus  ;  as  1  approach  the  paper  to  that  point,  observe 
how  the  brightness  of  the  spot  of  light  increases, 
while  its  size  diminishes. 

Caroline.     That  must  be  occasioned  by  the  rays 


ON   THE  ANGLE  OF  VISION.  221 

becoming  closer  together.  I  think  ^-ou  hold  the  pa- 
per just  in  the  focus  now,  the  light  is  so  small  and 
dazzling — Oh,  Mrs.  B.,  the  paper  has  taken  fire! 

Airs.  B.  The  rays  of  light  cannot  be  concentra- 
ted, without,  at  the  same  time,  accumulating  a  propor- 
tional quantity  of  heat:  hence  concave  mirrors  have 
obtained  the  name  of  burning-mirrors. 

Emily.  I  have  often  heard  of  the  surprising  etfects 
of  burning-mirrors,  and  I  am  quite  dehghted  to 
understand  their  nature. 

Caroline.  It  cannot  be  the  true  focus  of  the  mir- 
ror at  which  the  rays  of  the  sun  unite,  for  as  they 
proceed  from  a  point,  they  must  fall  divergent  upon 
the  mirror. 

Mrs.  B.  Strictly  speaking,  they  certainly  do.  But 
when  rays  come  from  such  an  immense  distance  as 
the  sun,  their  divergence  is  so  trifling,  as  to  be  im- 
perceptible ;  and  they  may  be  considered  as  parallel : 
their  point  of  union  is,  therefore,  the  true  focus  of 
the  mirror,  and  there  the  image  of  the  object  is  re- 
presented. 

Now  that  I  have  removed  the  mirror  out  of  the  in- 
fluence of  the  sun's  rays,  if  I  place  a  burning  taper  in. 
the  focus,  how  will  its  light  be  reflected  ?     (Fig.  6.) 

Caroline.     That,  I  confess,  I  cannot  say. 

Mrs.  B.  The  ray  which  falls  in  the  direction  of 
the  axis  of  the  mirror,  is  reflected  back  in  the  same 
line  ;  but  let  us  draw  two  other  rays  from  the  focus, 
falling  on  the  mirror  at  B  and  F  ;  the  dotted  lines  are 
perpendicular  to  those  points,  and  the  two  rays  will 
therefore  be  reflected  to  A  and  E. 

Caroline.  Oh,  now  I  understand  it  clearly.  The 
rays  which  proceed  from  a  light  placed  in  the  focus 
of  a  concave  mirror  fall  div^ergent  upon  it,  and  are 
reflected  parallel.  It  is  exactly  the  reverse  of  the 
former  experiment,  in  which  the  sun's  rays  fell  pa- 
rallel on  the  mirror,  and  were  reflected^  to  a  focus. 

Mrs.  B.  Yes  :  when  the  incident  rays  are  paral- 
lel, the  reflected  rays  converge  to  a  focus  ;  when,  odl 
the  contrary,  the  incident  rays  proceed  from  the  fo« 
19* 


222  ON   THE  ANGLE  OF  VISION* 

cus,  they  are  reflected  parallel.  This  is  an  impor- 
tant law  of  optics,  and  since  you  are  now  acquainted 
with  the  principles  on  which  it  is  founded,  I  hope  that 
you  will  not  forget  it. 

Caroline.  I  am  sure  that  we  shall  not.  But,  Mrs. 
B.,  you  said  that  the  image  was  formed  in  the  focus 
of  a  concave  mirror  ;  yet  I  have  frequently  seen  glass 
concave  mirrors,  where  the  object  has  been  repre- 
sented within  the  mirror,  in  the  same  manner  as  in  a 
convex  mirror. 

Mrs.  B.  That  is  the  case  only  when  the  object  is 
placed  between  the  mirror  and  its  focus  ;  the  image 
then  appears  magnified  behind,  or,  as  you  call  it, 
nvithin  the  mirror. 

Caroline.  I  do  not  understand  why  the  image 
should  be  larger  than  the  object. 

Mrs.  B.  It  proceeds  from  the  convergent  properr 
ty  of  the  concave  mirror.  If  an  object,  A  B,  (fig.  7.) 
be  placed  between  the  mirror  and  its  focus,  the  rays 
from  its  extremities  fall  divergent  on  the  mirror,  and 
on  being  reflected,  become  less  divergent,  as  if  they 
proceeded  from  C :  to  an  eye  placed  in  that  situation 
the  image  will  appear  magnified  behind  the  mirror 
^t  a  b,  since  it  is  seen  under  a  larger  angle  than  the 
object.  . 

You  now,  I  hope,  understand  the  reflection  of  light 
by  opaque  bodies.  At  our  next  meeting  we  shall 
enter  upon  another  property  of  light,  no  less  interest* 
ing,  which  is  called  refraction. 


CONVERSATION  XVl: 


ON  REFRACTION  AND  COLOURS. 

Transmission  of  Light  by  Transparent  Bodies. — Re- 
fraction. — Refraction  of  the  Atmosphere. — Refrac- 
tion of  a  Lens. — Refraction  of  the  Prism. — Of  the 
Colours  of  Rays  of  Light. — Of  the  Colours  of  Bodies. 

MRS.  B.  The  refraction  of  light  will  furnish  the 
•subject  of  to-day's  lesson. 

Caroline.  That  is  a  property  of  which  I  have  not 
the  faintest  idea. 

Mrs.  B.  It  is  the  effect  which  transparent  me- 
diums produce  on  light  in  its  passage  through  them. 
Opaque  bodies,  you  know,  reflect  the  rays,  and  trans- 
parent bodies  transmit  them;  but  it  is  found,  that  if  a 
ray,  in  passing  from  one  medium  into  another  of  dif- 
ferent density,  fall  obliquely,  it  is  turned  out  of  its 
course. 

Caroline.  It  must  then  be  acted  on  by  some  new- 
power,  otherwise  it  would  not  deviate  from  its  first 
direction. 

Mrs.  B.  The  power  which  causes  the  deviation 
of  the  ray  appears  to  be  the  attraction  of  the  denser 
medium.  Let  us  suppose  the  two  mediums  to  be  air 
and  water  ;  if  a  ray  of  light  passes  from  air  into  wa- 
ter, it  is  more  strongly  attracted  by  the  latter  on  ac- 
count of  its  superior  density. 

Emily,  in  what  direction  does  the  water  attract- 
the  ray  ? 

Mrs.  B.  It  must  attract  it  perpendicularly  towards 
it,  Id  the  same  manner  as  gravity  acts  on  bodies. 


224  THE  REFRACTION    OF    LIGHT. 

If  then  a  ray  A  B,  (fig.  1.  Plate  XIX.)  fall  perpen- 
dicularly on  water,  the  attraction  of  the  water  acts  in 
the  same  direction  as  the  course  of  the  ray  ;  it  will 
not  therefore  cause  a  deviation,  and  the  ray  will  pro- 
ceed straight  on  to  E.  But  if  it  fall  obliquely,  as  the 
ray  C  B,  the  water  will  attract  it  out  of  its  course. 
Let  us  suppose  the  ray  to  have  approached  the  surface 
of  a  denser  medium,  and  that  it  there  begins  to  be  af- 
fected by  its  attraction  ;  this  attraction,  if  not  counter- 
acted by  some  other  power,  would  draw  it  perpen- 
dicularly to  the  water,  at  B  ;  but  it  is  also  impelled 
by  its  projectile  force,  which  the  attraction  of  the 
denser  medium  cannot  overcome  ;  the  ray,  therefore, 
acted  on  by  both  these  powers,  moves  in  a  direction 
between  them,  and  instead  of  pursuing  its  original 
course  to  D,  or  being  implicitly  guided  by  the  water 
to  E,  proceeds  towards  F,  so  that  the  ray  appears  bent 
or  broken. 

Caroline,  I  understand  that  very  well ;  and  is  not 
this  the  reason  that  oars  appear  bent  in  water? 

Ah's.  B.  It  is  owing  to  the  refraction  of  the  rays 
reflected  by  the  oar  ;  but  this  is  in  passing  from  a 
dense  to  a  rave  medium,  for  you  know  that  the  rays, 
by  means  of  which  you  see  the  oar,  pass  from  water 
into  air. 

Emily.  But  I  do  not  understand  why  a  refraction 
takes  place  when  a  ray  passes  from  a  dense  into  a 
rare  medium  ;  I  should  suppose  that  it  would  be  ra- 
ther less,  than  more,  attracted  by  the  latter. 

Mrs,  B.  And  it  is  precisely  on  that  account  that 
the  ray  is  refracted.  C  B,  fig.  2.  represents  a  ray 
passing  obliquely  from  glass  into  water  :  glass  being 
the  denser  medium,  the  ray  will  be  more  strongly  at- 
tracted by  that  which  it  leaves  than  by  that  which  it 
enters.  The  attraction  of  the  glass  acts  in  the  direc- 
tion A  B,  while  the  impulse  of  projection  would  carry 
the  ray  to  F  ;  it  moves,  therefore,  between  these  di- 
rections towards  D. 

Emily.  So  that  a  contrary  refraction  takes  place 
when  a  ray  passes  from  a  dense  into  a  rare  mediunk. 


a        i  a 


JHT  a^lVTd 


T  •%■ 


THE  REFRACTION    OF    LIGHT.  22j 

Caroline.  But  does  not  the  attraction  of  the  denser 
medium  affect  the  ray  before  it  touches  it  ? 

Mrs.  B.  The  distance  at  which  the  attraction  of 
the  denser  medium  acts  upon  a  ray  is  so  small  as  to 
be  insensible  ;  it  appears  therefore  to  be  refracted 
only  at  the  point  at  which  it  passes  from  one  medium 
to  the  other. 

Now  that  you  understand  the  principle  of  refrac* 
tion,  I  will  show  you  the  refraction  of  a  real  ray  of 
light.  Do  you  see  the  flower  painted  at  the  bottom 
of  the  inside  of  this  tea-cup  ?     (Fig.  3.) 

Emily.  Yes. — But  now  you  have  moved  it  just 
out  of  sight,  the  rim  of  the  cup  hides  it. 

Mrs.  B.  Do  not  stir.  I  will  fill  the  cup  with  wa- 
ter, and  you  will  see  the  flower  again. 

Emily.  I  do  indeed  !  Let  me  try  to  explain  this  : 
when  you  draw  the  cup  from  me  so  «as  to  conceal  the 
tiower,  the  rays  reflected  by  it  no  longer  met  my 
eyes,  but  were  directed  above  them  ;  but  now  that 
you  have  filled  the  cup  with  water,  they  are  refracted 
by  the  attraction  of  the  water,  and  bent  downwards, 
so  as  again  to  enter  my  eyes. 

Mrs.  B.  You  have  explained  it  perfectly  :  fig.  3. 
will  help  to  imprint  it  on  your  memory.  You  must 
observe  that  when  the  flower  becomes  visible  by  the 
refraction  of  the  ray,  you  do  not  see  it  in  the  situation 
which  it  really  occupies,  but  an  image  of  the  flower 
higher  in  the  cup  ;  for  as  objects  always  appear  to 
be  situated  in  the  direction  of  the  rays  which  enter 
the  eye,  the  flower  will  be  seen  in  the  direction  of 
the  reflected  ray  at  B. 

Emily.  Then,  when  we  see  the  bottom  of  a  clear 
stream,  of  water,  the  rays  which  it  reflects  being  re- 
fracted in  their  passage  from  the  water  into  the  air, 
will  make  the  bottom  appear  higher  than  it  really  is. 

Mrs.  B.  And  the  water  will  consequently  appear 
more  shallow.  Accidents  have  frequently  been  oc- 
casioned by  this  circumstance  ;  and  boys  who  are  in 
the  habit  of  bathing  should  be  cautioned  not  to  trust 
to  the  apparent  shallowness  of  water,  as  it  will  always 


226  THE  REFRACTION    OF    LIGHT. 

prove  deeper  than  it  appears  ;  unless,  indeed,  they 
view  it  from  a  boat  on  the  water,  which  will  enable 
them  to  look  perpendicularly  upon  it ;  when  the  rays 
from  the  bottom  passing  perpendicularly,  no  refrac- 
tion will  take  place. 

The  retraction  of  light  prevents  our  seeing  the 
heavenly  bodies  in  their  real  situation  :  the  light  they 
send  to  us  being  refracted  in  passing  into  the  atmos- 
phere, we  see  the  sun  and  stars  in  the  direction  of 
the  refracted  ray  ;  as  described  in  tig.  4.  Plate  XIX., 
the  dotted  line  represents  the  extent  of  the  atmos- 
phere, above  a  portion  of  the  earth,  E  B  E  :  a  ray 
of  light  coming  from  the  sun  S,  falls  obliquely  on  it  at 
A,  and  is  refracted  to  B  ;  then,  since  we  see  the  ob- 
ject in  the  direction  of  the  refracted  ray,  a  spectator 
at  B  will  see  an  image  of  the  sun  at  C,  instead  of  the 
real  object  at  S. 

Eiuily.  But  if  the  sun  were  immediately  over  our 
heads,  its  Fays,  falling  perpendicularly  on  the  atmos- 
phere, would  not  be  refracted,  and  we  should  then  see 
the  real  sun  in  its  true  situation. 

Mrs.  B.  You  must  recollect  that  the  sun  is  verti- 
cal only  to  the  inhabitants  of  the  torrid  zone  ;  its 
rays,  therefore,  are  always  refracted  in  these  cli- 
mates. There  is  also  another  obstacle  to  our  seeing 
the  heavenly  bodies  in  their  real  situations  :  light, 
though  it  moves  with  extreme  velocity,  is  about  eight 
minutes  and  a  half  in  its  passage  from  the  sun  to  the 
earth  :  therefore,  when  the  rays  reach  us,  the  sun 
must  have  quitted  the  spot  he  occupied  on  their  de- 
parture ;  yet  we  see  him  in  the  direction  of  those 
rays,  and  consequently  in  a  situation  which  he  had 
abandoned  eight  minutes  and  a  half  before. 

Emily.  When  you  speak  of  the  sun's  motion,  you 
mean,  I  suppose,  his  apparent  motion,  produced  by 
the  diurnal  motion  of  the  earth. 

Mrs.  B.  No  doubt;  the  effect  being  the  same, 
whether  it  is  our  earth,  or  the  heavenly  bodies  which 
move  :  it  is  more  easy  to  represent  things  as  they  ap- 
pear to  be,  than  as  they  really  are. 


THE  REFRACTION    OF    LIGHTS  227 

Caroline.  During  the  morning,  then,  when  the 
sun  is  rising  towards  the  meridian,  we  must  rfrom  the 
length  of  time  the  light  is  in  reaching  us)  see  an 
image  of  the  sun  below  that  spot  which  it  really  oc- 
cupies. 

Emily.  But  the  refraction  of  the  atmosphere  coun- 
teracting this  effect,  we  may  perhaps,  between  the 
two,  see  the  sun  in  its  real  situation. 

Caroline.  And  in  the  afternoon,  when  the  sun  is 
sinking  in  the  west,  refraction  and  the  length  of  time 
which  the  light  is  in  reaching  the  earth,  will  conspire 
to  render  the  image  of  the  sun  higher  than  it  really  is* 

Mrs.  B.  The  refraction  of  the  sun's  rays  by  the 
atmosphere  prolongs  our  days,  as  it  occasions  our 
seeing  an  image  of  the  sun,  both  before  he  rises  and 
after  he  sets;  for  below  the  horizon,  he  still  shines 
upon  the  atmosphere,  and  his  rays  are  thence  refract- 
ed to  the  earth.  So  likewise  we  see  an  image  of  the 
sun  before  he  rises,  the  rays  that  previously  fall  upon 
the  atmosphere  being  reflected  to  the  earth. 

Caroline.  On  the  other  hand,  we  must  recollect 
that  light  is  eight  minutes  and  a  half  on  its  journey  ;  so 
that,  by  the  time  it  reaches  the  earth,  the  sun  may 
perhaps  be  risen  above  the  horizon. 

Emily.  Pray  do  not  glass  windows  refract  the 
light. 

Mrs.  B.  They  do  ;  but  this  refraction  is  not  per- 
ceptible, because,  in  passing  through  a  pane  of  glass 
the  rays  suffer  two  refractions,  which  being  in  contra- 
ry directions,  produce  the  same  effect  as  if  no  refrac- 
tion had  taken  place. 

Emily.     I  do  not  understand  that. 

Mrs.  B.  Fig.  b.  Plate  XIX.  will  make  it  clear  to 
you  :  A  A  represents  a  thick  pane  of  glass  seen  edge- 
ways. When  the  ray  B  approaches  the  glass  at  C,  it 
is  refracted  by  it ;  and  instead  of  continuing  its  course 
in  the  same  direction,  as  the  dotted  line  describes,  it 
passes  through  the  pane  to  D  ;  at  that  point  returning 
into  the  air,  it  is  again  refracted  by  the  glad's,  but  in  a 
contrarv  direction  t©  the  first  refraction,  and  in  conse- 


228  THE  REFRACTION    OF    LIGHT. 

quence  proceeds  to  E.  Now  you  must  observe  that 
the  ray  B  C  and  the  ray  D  E  being  parallel,  the  ii^ht 
does  not  appear  to  have  suffered  any  refraction. 

Emily  So  that  the  effect  which  takes  place  on  the 
ray  entering  the  glass,  is  undone  on  i  s  quitting  it. 
Or,  to  express  myself  more  scientifically,  when  a  ray 
of  light  passes  from  one  medium  into  another,  an^^^ 
through  that  into  the  first  again,  the  two  refractiorfs 
being  equal  and  in  opposite  directions,  no  sensible 
effect  is  produced. 

Mrs.  B.  Thi^  is  the  case  when  the  two  surfaces 
of  the  refracting  medium  are  parallel  to  each  other; 
if  they  are  not,  the  two  refractions  may  be  made  in  the 
same  direction,  as  1  shall  show  you. 

When  parallel  rays  (fig.  6.)  fall  on  a  piece  of  glass 
having  a  double  convex  surface,  and  wl)ich  is  called  a 
Lens,  that  only  which  f  tils  in  the  direction  of  the  axis 
of  the  lens  is  perpentlicular  to  the  surface  ;  the  other 
rays  falling  obliquely  are  refracted  towards  the  axis, 
and  will  meet  at  a  point  beyond  the  lens,  called  its 
focus. 

Of  the  three  rays,  A  B  C,  which  fdl  on  the  lens  D 
E,  the  rays  A  and  C  are  refracted  in  their  passage 
through  it,  to  a,  and  r,  and  on  quitting  the  lens  they 
undergo  a  second  refraction  in  the  same  direction, 
which  unites  them  with  the  ray  B,  at  the  focus  F. 

Einilij.  And  what  is  the  distance  of  the  focus  from 
the  surface  of  the  lens  ? 

Mrs.  B.  The  focal  distance  depends  both  upon  the 
form  of  the  lens,  and  of  the  refractive  power  of  the 
substance  of  which  it  is  made  :  in  a  glaes  lens,  both 
sides  of  wliich  are  equally  convex,  the  focus  is  situated 
nearly  at  the  centre  of  the  sphere  of  which  the  sur- 
fiice  of  the  lens  forms  a  portion  ;  it  is  at  the  distance, 
therefore,  of  the  radius  of  the  sphere. 

There  are  lenses  of  various  forms,  as  you  will  find 
described  in  fig.  1.  Plate  XX.  The  property  of  those 
which  have  a  convex  surface  is  to  collect  the  rays  of 
light  to  a  focus  ;  and  of  those  which  have  a  concave 
surface,  on  the  contrary,  to  disperse  them.  For  the  rays 


-%•  ^■ 


PLATE.  XT. 


m 


THE  REFRACTION   OF   LIOHT#  '      2^ 

A  C  falling  on  the  concave  lens  X  Y,  (fig.  7.  Plate 
XIX.)  instead  of  converging  towards  the  ray  B,  wliicK 
falls  on  the  axis  of  the  lens,  will  each  be  attracted  to- 
wards the  thick  edges  of  the  lens,  both  on  entering 
and  quitting  it,  and  will,  therefore,  by  the  first  re- 
fraction, be  made  to  diverge  to  a,  c,  and  by  the  second 
to  </,  e. 

Caroline,  And  lenses  which  have  one  side  flat  and 
the  other  convex  or  concave,  Jis  A  and  B,  fig.  1 .  Plate 
XX.,  are,  I  suppose,  less  powerful  in  their  refrac- 
tions ? 

Mrs.  B.  Yes  ;  they  are  called  plano-convex  and 
plano-concave  lenses  :  the  focus  of  the  former  is  at 
the  distance  of  the  diameter  of  a  sphere,  of  which  the 
convex  surface  of  the  lens  forms  a  portion  ;  as  repre- 
sented in  fig.  2.  Plate  XX.  The  three  parallel  rays, 
ABC,  are  brought  to  a  focus  by  the  plano-convex 
lens  X  Y  at  F, 

I  must  now  explain  to  you  the  refraction  of  a  trian- 
gular piece  of  glass,  called  a  prism.  (Fig.  3.) 

Emily.  The  three  sides  of  this  glass  are  flat  :  it 
cannot,  therefore,  bring  the  rays  to  a  focus  ;  nor  do 
I  suppose  that  its  refraction  will  be  similar  to  that  of 
a  flat  pane  of  glass,  because  it  has  not  two  sides  paral- 
lel ;  I  cannot,  therefore,  conjecture  what  eflect  the 
refraction  of  a  prism  can  produce. 

Mrs  B.  The  refractions  of  the  light,  on  entering 
and  on  quitting  the  prism,  are  both  in  the  same  direc- 
tion. (Fig-  3.)  On  entering  the  prism  P,  the  ray 
A  is  refracted  from  B  to  C,  and  on  quitting  it  from  C 
toD. 

1  will  show  you  this  in  nature  ;  but  for  this  purpose 
it  will  be  advisable  to  close  the  window-shutters,  and 
admit,  through  the  small  aperture,  a  ray  of  light,  which 
I  shall  refract  by  means  of  this  prism. 

Caroline.  Oh,  what  beautiful  colours  are  repre- 
sented on  the  opposite  wall !  There  are  all  the  co- 
lours of  the  rainbow,  and  with  a  brightness  1  never 
saw  equalled.     (Fig.  4.  Plate  XX.) 

Emiiy.     i  have  seen  an  effect,  in  some  respects  si- 
20 


230       ON  REFRACTION  AND  COLOURS. 

milar  to  this,  produced  by  the  rays  of  the  sun  shining 
upon  glass  lustres  ;  but  how  is  it  possible  that  a  piece 
of  white  glass  can  produce  such  a  variety  of  brilliant 
colours  ? 

Mrs.  B.  The  colours  are  not  formed  by  the  prism, 
but  existed  in  the  ray  previous  to  its  refraction. 

Caroline.  Yet,  before  its  refraction  it  appeared 
perfectly  white. 

Mrs.  B.  The  white  rays  of  the  sun  are  composed 
of  coloured  rays,  which,  when  blended  together,  ap- 
pear colourless  or  white. 

Sir  Isaac  Newton,  to  whom  we  are  indebted  for  the 
most  important  discoveries  respecting  light  and  co- 
lours, was  the  first  who  divided  a  white  ray  of  light, 
and  found  it  to  consist  of  an  assemblage  of  coloured 
rays,  which  formed  an  image  upon  the  wall,  such  as 
you  now  see  exhibited,  (fig  4.)  in  which  are  display- 
ed the  following  series  of  colours  :  red,  orange,  yel- 
low, green,  blue,  indigo,  and  violet. 

Emily.  But  how  does  a  prism  separate  these  co- 
loured rays  ? 

Mrs.  B.  By  refraction.  It  appears  that  the  co- 
loured rays  have  different  degrees  of  refrangibility  ; 
in  passing  through  the  prism,  therefore,  they  take 
different  directions  according  to  their  susceptibility  of 
refraction.  The  violet  rays  deviate  most  from  their 
original  course  ;  they  appear  at  one  of  the  ends  of 
the  spectrum  A  B  :  contiguous  to  the  violet  are  the 
blue  rays,  being  those  which  have  somewhat  less  re- 
frangibility ;  then  follow,  in  succession,  the  green, 
yellow,  orange,  and,  lastly,  the  red,  which  are  the 
least  refrangible  of  the  coloured  rays. 

Caroline.  I  cannot  conceive  how  these  colours, 
mixed  together,  can  become  white  ? 

Mrs.  B.  That  I  cannot  pretend  to  explain  ;  but 
it  is  a  fact,  that  the  union  of  these  colours,  in  the  pro- 
portions in  which  they  appear  in  the  spectrum,  pro- 
duce in  us  the  idea  of  whiteness.  If  you  paint  a  card 
in  compartments  with  these  seven  colours,  and  whirl 
it  rapidly  on  a  pin,  it  will  appear  white. 


ox  UEfKACilON  AND  COLOURS.       231 

But  a  more  decisive  proof  of  the  composition  of  a 
white  ray  is  afl'orded  by  re-uniting  these  coloured  rays, 
and  forming  with  them  a  ray  of  white  light. 

Caroline.  If  you  can  take  a  ray  of  white  light  to 
pieces,  and  put  it  together  again,  1  shall  be  quite 
satisfied. 

Mrs.  B.  This  can  be  done  by  letting  the  coloured 
rays,  which  have  been  separated  by  a  prism,  fall 
upon  a  lens,  which  will  converge  them  to  a  focus  ; 
and  if,  when  thus  re-united,  we  lind  that  they  appear 
white,  as  they  did  before  refraction,  I  hope  that  you 
will  be  convinced  that  the  white  rays  are  a  compound 
of  the  several  coloured  rays.  The  prism  P,  you  see, 
;fig.  5.)  separates  a  ray  of  white  light  into  seven  co- 
loured rays,  and  the  lens  L  L  brings  them  to  a  focus 
at  F,    where  they  again  appear  white. 

Caroline.  You  succeed  to  perfection  :  this  is  in- 
deed a  most  interesting  and  conclusive  experiment. 

Emily.  Yet,  Mrs.  B.,  I  cannot  help  thinking,  that 
there  may  perhaps  be  but  three  distinct  colours  in 
the  spectrum,  red,  yellow,  and  blue  ;  and  that  the 
four  others  may  consist  of  two  of  these  colours  blend- 
ed together  ;  for,  in  painting,  we  find  that  by  mixing 
red  and  yellow,  we  produce  orange  ;  with  different 
proportions  of  red  and  blue,  we  make  violet  or  any 
shade  of  purple  ;  and  yellow  and  blue  form  green. 
Now  it  is  very  natural  to  suppose,  that  the  refraction 
of  a  prism  may  not  be  so  perfect  as  to  separate  the 
coloured  rays  of  light  completely,  and  that  those 
which  are  contiguous  in  order  of  refrangibility  may 
encroach  on  each  other,  and  by  mixing  produce  the 
intermediate  colours,  orange,  green,  violet,  and  in- 
digo. 

Mrs.  B.  Your  observation  is,  I  believe,  neither 
quite  wrong,  nor  quite  right.  Dr.  Wollaston,  who 
has  refracted  light  in  a  more  accurate  manner  than 
had  been  previously  done,  by  receiving  a  very  nar- 
row line  of  light  on  a  prism,  found  that  it  formed  a 
spectrum,  consisting  of  rays  of  four  colours  only  ; 
but  they  were  not  exactly  those  you  have  named  as 


J3^  ON    nEFRACTION  AND  COLOUR^. 

primitive  colours,  for  they  consisted  of  red,  green < 
blue,  and  violet.  A  very  narrow  line  of  yellow  was 
visible  at  the  limit  of  the  red  and  green,  which  Dr. 
Wollaston  attributed  to  the  overlapping  of  the  edges 
of  the  red  and  green  light. 

Caroline.  But  red  and  green  mixed  together  do 
not  produce  yellow. 

Mrs.  B.  Not  in  painting  :  but  it  may  be  so  in  the 
primitive  rays  of  the  spectrum.  Dr.  Wollaston  ob- 
served that,  by  increasing  the  breadth  of  the  aperture 
by  which  the  line  of  light  was  admitted,  the  space  oc- 
cupied by  each  coloured  ray  in  the  spectrum  was  aug- 
mented, in  proportion  as  each  portion  encroached  on 
the  neighbouring  colour  and  mixed  with  it ;  so  that 
the  intervention  of  orange  and  yellow,  between  the 
red  and  green,  is  owing,  he  supposes,  to  the  mixture 
of  these  two  colours,  and  the  blue  is  blended  on  the 
ene  side  with  the  green,  and  on  the  other  with  the 
violet,  forming  the  spectrum  as  it  was  originally  ob- 
served by  Sir  Isaac  Newton,  and  which  1  have  just 
shown  you. 

The  rainbow,  which  exhibits  a  series  of  colours  so 
analogous  to  those  of  the  spectrum,  is  formed  by  the 
refraction  of  the  sun's  rays  in  their  passage  through  a 
shower  of  rain,  every  drop  of  which  acts  as  a  prism, 
in  separating  the  coloured  rays  as  they  pass  through 
it. 

Emily.  Pray,  Mrs.  B.,  cannot  the  sun's  rays  be 
collected  to  a  focus  by  a  lens  in  the  same  manner  as 
they  are  by  a  concave  mirror  ? 

Mrs.  B.  No  doubt  the  same  effect  is  produced  by 
the  refraction  of  a  lens  as  by  the  retlection  of  a  con- 
cave mirror :  in  the  first,  the  rays  pass  through  the 
glass  and  converge  to  a  focus  behind  it ;  in  the  latter, 
they  are  reflected  from  the  mirror,  and  brought  to  a 
focus  before  it.  A  lens,  when  used  for  the  purpose  of 
collecting  the  sun's  rays,  is  called  a  burning  glass. 
The  sun  now  shines  very  bright ;  if  we  let  the  rays 
fall  on  this  lens  you  will  perceive  the  focus. 

Emily.     Oh  yes :  the  point  of  union  of  the  rays  is 


ON  REFRACTION  AND  COLOURS.      23S 

very  luminous.  I  will  hold  a  piece  of  paper  in  the 
focus,  and  see  if  it  will  take  fire.  The  spot  of  light  is 
extremely  brilHant,  but  the  paper  does  not  burn  ? 

Mr».  B.  Try  a  piece  of  brown  paper  ; — that  you 
see  takes  fire  almost  immediately. 

Caroline.  This  is  surprising  ;  for  the  light  appear- 
ed to  shine  more  intensely  on  the  white  than  on  the 
brown  paper. 

Mrs.  B.  The  lens  collects  an  equal  number  of 
Fays  to  a  focus,  whether  you  hold  the  white  or  the 
brown  paper  there  ;  but  the  white  paper  appears 
more  luminous  in  the  focus,  because  most  of  the  rays, 
instead  of  entering  into  the  paper,  are  reflected  by  it : 
and  this  is  the  reason  that  the  paper  is  not  burnt ; 
whilst,  on  the  contrary,  the  brown  paper,  which  ab- 
sorbs more  light  than  it  reflects,  soon  becomes  heate4 
and  takes  fire. 

Caroline.  This  is  extremely  curious  ;  but  why 
should  brown  paper  absorb  more  rays  than  white  pa- 
per ? 

Mrs.  B.  I  am  far  from  being  able  to  give  a  satis- 
factory answer  to  that  question.  We  can  form  but 
mere  conjecture  on  this  point ;  and  suppose  that 
the  tendency  to  absorb,  or  reflect  rays,  depends  on 
the  arrangement  of  the  minute  particles  of  the  bo- 
dy, and  that  this  diversity  of  arrangement  renders 
some  bodies  susceptible  of  reflecting  one  coloured 
ray,  and  absorbing  the  others  ;  whilst  other  bodies 
have  a  tendency  to  reflect  all  the  colours,  and  others 
again,  to  absorb  them  all. 

Emily.  And  how  do  you  know  which  colours  bo- 
dies have  a  tendency  to  reflect :  or  which  to  absorb  ? 

Mrs.  B.  Because  a  body  always  appears  to  be  of 
the  colour  which  it  reflects  ;  for,  as  we  see  only  by 
reflected  rays,  it  can  appear  but  of  the  colour  of  those 
rays. 

Caroline.  But  we  see  all  bodies  of  their  own  natu- 
ral colour,  Mrs.  B.  ;  the  grass  and  trees,  green  ;  the 
sky,  blue  ;  the  flowers,  of  various  hues. 

Mrs.  B.  True  ;  but  why  is  the  grass  green  ?-— 
20* 


234  ox  REFRACTION  AM)  COLOUR;^. 

because  it  absorbs  all  except  the  green  rays  ;  it  is 
therefore  these  only  which  the  grass  and  trees  reflect 
to  our  eyes,  and  which  makes  them  appear  green. 
The  sky  and  flowers,  in  the  same  manner,  reflect  the 
various  colours  of  which  they  appear  to  us  ;  the  rose, 
the  red  rays  ;  the  violet,  the  blue  ;  the  jonquil,  the 
yellow,  &c. 

Caroline.  But  these  are  the  permanent  colours  of 
the  grass  and  flowers,  whether  the  sun's  rays  shine  on 
them  or  not. 

Mrs.  B.  Whenever  you  see  those  colours,  the 
flowers  must  be  illumined  by  some  hght ;  and  light, 
from  whatever  source  it  proceeds,  is  of  the  same  na- 
ture, composed  of  the  various  coloured  rays,  which 
paint  the  grass,  the  flowers,  and  every  coloured  ob- 
ject in  nature. 

Caroline.  But,  Mrs.  B.,  the  grass  is  green,  and  the 
flowers  are  coloured,  whether  in  the  dark,  or  expo- 
sed to  the  light  ? 

Mrs.  B.     Why  should  you  think  so  ? 

Caroline.     It  cannot  be  otherwise. 

Mrs.  B.  A  most  philosophical  reason  indeed  1 
But,  as  I  never  saw  them  in  the  dark,  you  will  allow 
me  to  dissent  from  your  opinion. 

Caroline.  What  colour  do  you  suppose  them  to  be, 
then,  in  the  dark  ? 

Mrs.  B.  None  at  all  :  or  black,  which  is  the  same 
thing.  You  can  never  see  objects  without  light. 
Light  is  composed  of  colours,  therefore  there  can  be 
no  light  without  colours  ;  and  though  every  object  is 
black,  or  without  colour  in  the  dark,  it  becomes  co- 
loured as  soon  as  it  becomes  visible.  It  is  visible, 
indeed,  but  by  the  coloured  rays  which  it  reflects  ; 
therefore  we  can  see  it  only  when  coloured. 

Caroline.  All  you  say  seems  very  true,  and  I  know 
not  what  to  object  to  it ;  yet  it  appears  at  the  same 
time  incredible  !  What,  Mrs.  B.,  are  we  all  as  black 
as  negroes,  in  the  dark  ?  you  make  me  shudder  at 
the  thought. 

Mrs.  B,     Your  vanity  need  not  be  alarmed  at  the- 


ON  REFRACTION  AND  COLOURS.      235 

idea,  as  you  are  certain  of  never  being  seen  in  that 
state. 

Caroline.  That  is  some  consolation,  undoubtedly  ; 
but  what  a  melancholy  reflection  it  is,  that  all  nature, 
which  appears  so  beautifully  diversified  with  colours, 
should  be  one  uniform  mass  of  blackness  ! 

Mrs.  B.  Is  nature  less  pleasing  for  being  colour- 
ed, as  well  as  illumined  by  the  rays  of  light ;  and  are 
colours  less  beautiful,  for  being  accidental,  rather 
than  essential  properties  of  bodies  ? 

Providence  appears  to  have  decorated  nature  with 
the  enchanting  diversity  of  colours,  which  we  so 
much  admire,  for  the  sole  purpose  of  beautifying  the 
scene,  and  rendering  it  a  source  of  pleasurable  enjoy- 
ment :  it  is  an  ornament  which  embellishes  nature 
whenever  we  behold  her.  What  reason  is  there  to 
regret  that  she  does  not  wear  it  when  she  is  invisible  ? 

Emily.  1  confess,  Mrs.  B.,  that  I  have  had  my 
doubts,  as  well  as  Caroline,  though  she  has  spared 
me  the  pains  of  expressing  them  ;  but  1  have  just 
thought  of  an  experiment,  which,  if  it  succeeds,  will, 
1  am  sure,  satisfy  us  both.  It  is  certain  that  we  can- 
not see  bodies  in  the  dark,  to  know  whether  they  have 
then  any  colour.  But  we  may  place  a  coloured  body 
in  a  ray  of  light,  which  has  been  refracted  by  a 
prism  ;  and  if  your  theory  is  true,  the  body,  of  what- 
ever colour  it  naturally  is,  must  appear  of  the  colour 
of  the  ray  in  which  it  is  placed  ;  for  since  it  receives 
no  other  coloured  rays,  it  can  reflect  no  others. 

Caroline.  Oh  !  that  is  an  excellent  thought,  Emily  ; 
will  you  stand  the  test,  Mrs.  B.  ? 

Mrs.  B.  1  consent  :  but  we  must  darken  the  room, 
and  admit  only  the  ray  which  is  to  be  refracted  ; 
otherwise,  the  white  rays  will  be  reflected  on  the 
body  under  trial,  from  various  parts  of  the  room. 
With  what  do  you  choose  to  make  the  experiment  ? 

Caroline.  '1  his  rose  :  look  at  it,  Mr.*.  B.,  and  tell 
me  whether  it  is  possible  to  deprive  it  of  its  beautiful 
colour  ? 

Mrs.  B.     We  shall  see. — I   expose  it  first  to  the 


236       ©X  REFRACTIOX  AND  COLOURS. 

red  rays,  and  the  flower  appears  of  a  more  brilliant 
hue  ;  but  observe  the  green  leaves — 

Caroline.  They  appear  neither  red  nor  green  ; 
but  of  a  dingy  brown  with  a  reddish  glow  ! 

Mrs.  B.  They  cannot  be  green,  because  they 
have  no  green  rays  to  reflect ;  neither  are  they  red, 
because  green  bodies  absorb  most  of  the  red  rays. 
But  though  bodies,  from  the  arrangement  of  their 
particles,  have  a  tendency  to  absorb  some  rays,  and 
reflect  others,  yet  it  is  not  natural  to  suppose,  that 
bodies  are  so  perfectly  uniform  in  their  arrangement, 
as  to  reflect  only  pure  rays  of  one  colour,  and  per- 
fectly absorb  the  others  :  it  is  found,  on  the  contrary, 
that  a  body  reflects,  in  great  abundance,  the  rays 
which  determine  its  colour,  and  the  others  in  a  greater 
or  less  degree,  in  proportion  as  they  are  nearer  or 
further  from  its  own  colour,  in  the  order  of  refrangi- 
bility.  The  green  leaves  of  the  rose,  therefore,  will 
reflect  a  few  of  the  red  rays,  which,  blended  with 
their  natural  blackness,  give  them  that  brown  tinge  : 
if  they  reflected  none  of  the  red  rays,  they  would  ap- 
pear perfectly  black.  Now  I  shall  hold  the  rose  in 
the  blue  rays — 

Caroline.  Oh,  Emily,  Mrs.  B.  is  right!  look  at 
the  rose  :  it  is  no  longer  red,  but  of  a  dingy  blue  co- 
lour. 

Emily.  This  is  the  most  wonderful  of  any  thing  we 
have  yet  learnt.  But,  Mrs.  B.,  what  is  the  reason 
that  the  green  leaves  are  of  a  brighter  blue  than  the 
rose  ? 

Mrs.  B.  The  green  leaves  reflect  both  blue  and 
yellow  rays,  which  produces  a  green  colour.  They 
are  now  in  a  coloured  ray,  which  they  have  a  ten- 
dency to  reflect ;  the}^  therefore,  reflect  more  of 
the  blue  rays  than  the  rose,  (which  naturally  absorbs 
that  colour,)  and  will,  of  course,  appear  of  a  brighter 
blue. 

Emily.  Yet,  in  passing  the  rose  through  the  differ- 
ent colours  of  the  spectrum,  the  flower  takes  them 
more  readily  than  the  leaves. 


ON  REFRACTION  AND  COLOURS.       237 

.Mrs,  B.  Because  the  flower  is  of  a  paler  hue. 
Bodies  which  reflect  all  the  rays  are  white  ;  those 
which  absorb  them  all  are  black  :  between  these  ex- 
tremes, the  body  appears  lighter  or  darker,  in  pro- 
portion to  the  quantity  of  rays  they  reflect  or  absorbs 
This  rose  is  of  a  pale  red  :  it  approaches  nearer  to 
white  than  black  ;  it  therefore  reflects  rays  more 
abundantly  than  it  absorbs  them. 

Emily.  But  if  a  rose  has  so  strong  a  tendency  ta 
reflect  rays,  I  should  have  imagined  that  it  would  be 
of  a  deep  red  colour. 

Mrs.  B.  1  mean  to  say,  that  it  has  a  general  ten- 
dency to  reflect  rays.  Pale-coloured  bodies  reflect 
all  the  coloured  rays  to  a  certain  degree,  which  pro- 
duces their  paleness,  approaching  to  whiteness  :  but 
one  colour  they  reflect  more  than  the  rest ;  this 
predominates  over  the  white,  and  determines  the 
colour  of  the  body.  Since,  then,  bodies  of  a 
pale  colour  in  some  degree  reflect  all  the  rays  of  light, 
in  passing  through  the  various  colours  of  the  spec- 
trum, they  will  reflect  them  all  with  tolerable  brilli- 
ancy ;  but  will  appear  most  vivid  in  the  ray  of  their 
natural  colour.  The  green  leaves,  on  the  contrary, 
are  of  a  dark  colour,  bearing  a  stronger  resemblance 
to  black  than  to  white ;  they  have,  therefore,  a 
greater  tendency  to  absorb  than  to  reflect  rays  ;  and 
reflecting  very  ie^w  of  any  but  the  blue  and  yellow 
rays,  they  will  appear  dingy  in  passing  through  the 
other  colours  of  the  spectrum. 

Caroline.  They  must,  however,  reflect  great 
quantities  of  the  green  rays,  to  produce  so  deep  a  co- 
lour. 

Mrs.  B.  Deepness  or  darkness  of  colour  proceeds 
rather  from  a  deficiency  than  an  abundance  of  reflect- 
ed rays.  Remember  that  bodies  are,  of  themselves, 
black  ;  and  if  a  body  reflects  only  a  few  green  rays, 
it  will  appear  of  a  dark  green,  it  is  the  brightness  and 
intensity  of  the  colour  which  show  that  a  great  quan- 
tity of  rays  are  reflected. 

Emily.     A  white  body,  then,  which  reflects  all  the 


238  ox  IlEFRACTIOX  AND  COLOURS. 

rays,  will  appear  equally  bright  in  all  the  colours  ot 
the  spectrum. 

Mrs.  B.  Certainly.  And  this  is  easily  proved  by 
passing  a  sheet  of  white  paper  through  the  rays  of  the 
spectrum. 

Caroline.  What  is  the  reason  that  blue  often  ap- 
pears green  by  candle-light? 

Mrs.  B.  The  light  of  a  candle  is  not  so  pure  as 
that  of  the  sun  :  it  has  a  yellowish  tinge,  and  when 
refracted  by  the  prism,  the  yellow  rays  predominate  ; 
and  as  blue  bodies  reflect  the  yellow  rays  in  the  next 
proportion,  (being  next  in  order  of  refrangibility,)  the 
superabundance  of  yellow  rays  gives  to  blue  bodies  a 
greenish  hue. 

Caroline.  Candle-light  must  then  give  to  all  bodies 
a  yellowish  tinge,  from  the  excess  of  yellow  rays  : 
and  yet  it  is  a  common  remark,  that  people  of  a  sal- 
low complexion  appear  fairer  or  whiter  by  candle- 
light. 

Mrs.  B.  The  yellow  cast  of  their  complexion  is 
not  so  striking  when  every  object  has  a  yellow 
linge. 

Emily.  Pray,  why  does  the  sun  appear  red  through 
a  fog? 

Mrs.  B.  It  is  supposed  to  be  owing  to  the  red 
rays  having  a  greater  momentum,  which  gives  them 
power  to  traverse  so  dense  an  atmosphere.  For  the 
same  reason,  the  sun  generally  appears  red  at  rising 
and  setting  :  as  the  increased  quantity  of  atmosphere, 
which  the  oblique  rays  must  traverse,  loaded  with  the 
mists  and  vapours  which  are  usually  formed  at  those 
times,  prevents  the  other  rays  from  reaching  us. 

Caroline.  And,  pray,  why  are  the  skies  of  a  blue 
colour? 

Mrs.  B.  You  should  rather  say  the  atmosphere  ; 
for  the  sky  is  a  very  vague  term,  the  meaning  of 
which  it  would  be  difficult  to  define  philosophically. 

Caroline.  But  the  colour  of  the  atmosphere  should 
be  white,  since  aJl  the  rays  traverse  it  in  their  passage 
to  the  earth. 


ON  REFRACTION  AND  COLOURS.       239 

Mrs.  B.  Do  not  forsjet  that  we  see  none  of  the 
rays  which  pass  from  the  sun  to  the  earth,  excepting 
those  which  meet  our  eyes  ;  and  this  happens  only  if 
we  look  at  the  sun,  and  thus  intercept  the  rays,  in 
which  case,  you  know,  the  sun  appears  white.  The 
atmosphere  is  a  transparent  medium,  through  which 
the  sun's  rays  pass  freely  to  the  earth  ;  but  when  re- 
flected back  into  the  atmosphere,  their  momentum  is 
considerably  diminished  ;  and  they  have  not  all  of 
them  power  to  traverse  it  a  second  time.  The  mo- 
mentum of  the  blue  rays  is  least ;  these,  therefore, 
are  the  most  impeded  in  their  return,  and  are  chiefly 
reflected  by  the  atmosphere :  this  reflection  is  per- 
formed in  every  possible  direction  ;  so  that  whenever 
we  look  at  the  atmosphere,  some  of  these  rays  fall 
upon  our  eyes  ;  hence  we  see  the  air  of  a  blue  colour. 
If  the  atmosphere  did  not  reflect  any  rays,  though 
the  objects  on  the  surface  of  the  earth  would  be  illu- 
mined, the  skies  would  appear  perfectly  black. 

Caroline.  Oh,  how  melancholy  that  would  be  ;  and 
how  pernicious  to  the  sight,  to  be  constantly  viewing 
bright  objects  against  a  black  sky.  But  what  is  the 
reason  that  bodies  often  change  their  colour  ;  as 
leaves  which  wither  in  autumn,  or  a  spot  of  ink  which 
produces  an  iron-mould  on  linen  ? 

Mrs.  B.  It  arises  from  some  chemical  change, 
which  takes  place  in  the  internal  arrangement  of  the 
parts,  by  which  they  lose  their  tendency  to  reflect 
certain  colours,  and  acquire  the  power  of  reflecting 
others.  A  withered  leaf  thus  no  longer  reflects  the 
blue  rays  ;  it  appears,  therefore,  yellow,  or  has  a 
slight  tendency  to  reflect  several  rays  which  produce 
a  dingy  brown  colour. 

An  ink-spot  on  linen  at  first  absorbs  all  the  rays  ; 
but,  exposed  to  the  air,  it  undergoes  a  chemical 
change,  and  the  spot  partially  regains  its  tendency  to 
reflect  colours,  but  with  a  preference  to  reflect  the 
yellow  rays,  and  such  is  the  colour  of  the  iron-mould. 

Emily.  Bodies,  then,  far  from  being  of  the  colour 
which  they  appear  to  possess,  are  of  that  colour  which 


240       ON  REFRACTION  AND  COLOURb. 

they  have  the  greatest  aversion  to,  which  they  will 
not  incorporate  with,  but  reject  and  drive  from  them. 

Mrs.  B.  It  certainly  is  so  ;  though  1  scarcely  dare 
venture  to  advance  such  an  opinion,  whilst  Caroline 
is  contemplating  her  beautiful  rose. 

Caroline.  My  poor  rose  !  you  are  not  satisfied 
with  depriving  it  of  colour,  but  even  make  it  have  an 
aversion  to  it ;  and  1  am  unable  to  contradict  you. 

Emily.  Since  dark  bodies  absorb  more  solar  rays 
than  light  ones,  the  former  should  sooner  be  heated 
if  exposed  to  the  sun  ? 

Mrs.  B.  And  they  are  found  by  experience  to  be 
so.  Have  you  never  observed  a  black  dress  to  be 
warmer  than  a  white  one  ? 

Emily.  Yes,  and  a  white  one  more  dazzling :  the 
black  is  heated  by  absorbing  the  rays,  the  white  daz- 
zling by  reflecting  them. 

Caroline.  And  ihis  was  the  reason  that  the  brown 
paper  was  burnt  in  the  focus  of  the  lens,  whilst  the 
white  paper  exhibited  the  most  luminous  spot,  but 
did  not  take  fire. 

Mrs.  B.  It  was  so.  It  is  now  full  time  to  con- 
clude our  lesson.  At  our  next  meeting,  1  shall  give 
.you  a.  description  of  the  eye. 


TJLATE    irXJ. 


CONVERSATION  XVIf. 


OPTICS. 

ON  THE  STRUCTURE  OF  THE  EYE,  AND 
OPTICAL  INSTRUMENTS. 

Description  of  the  Eye. — Of  the  Image  on  the  Retina. — 
Refraction  of  the  Humours  of  the  Eye. — Of  the  Use 
of  Spectacles. — Of  the  Single  Microscope. — Of  the 
Double  Microscope. — Of  the  Solar  Microscope. — 
Magic  Lanthorn. — Refracting  lelescope. — Reflecting 
Telescope. 

MRS.  B.  The  body  of  the  eye  is  of  a  spherical 
form:  (fig.  1.  Phite  XXI.)  it  has  two  membranous 
coverings  ;  the  external  one,  «  a  a,  is  called  the  scle- 
rotica :  this  has  a  projection  in  that  part  of  the  eye 
which  is  exposed  to  view,  h  6,  which  is  called  the 
cornea,  because,  when  dried,  it  has  nearly  the  con- 
sistence of  very  fine  horn,  and  is  sufficiently  transpa- 
rent for  the  light  to  obtain  free  passage  through  it. 

The  second  membrane  which  lines  the  cornea,  and 
envelopes  the  eye,  is  called  the  choroid,  c  c  c;  this 
has  an  opening  in  front,  just  beneath  the  cornea, 
which  forms  the  pupil,  d  d,  through  which  the  rays 
of  light  pass  into  the  eye.  The  pupil  is  surrounded 
by  a  coloured  border,  called  the  iris,  e  e,  which,  by 
its  muscular  motion,  always  preserves  the  pupil  of  a 
circular  form,  whether  it  is  expanded  in  the  dark,  oi- 
contracted  by  a  strong  light.  This  you  wilLnndor^ 
stand  better  by  examining  fig.  2. 
"21 


242  OPTICS. 

Emily,  I  did  not  know  that  the  pupil  was  suscepu- 
ble  of  varying  its  dimensions. 

Mrs.  B.  The  construction  of  the  eye  is  so  admira- 
ble, that  it  is  capable  of  adapting  itself,  more  or  less, 
to  the  circumstances  in  which  it  is  placed.  In  a  faint 
light  the  pupil  dilates  so  as  to  receive  an  additional 
quantity  of  rays,  and  in  a  strong  light  it  contracts,  in 
order  to  prevent  the  intensity  of  the  light  from  injur- 
ing the  optic  nerve.  Observe  Emily's  eyes,  as  she 
gits  looking  towards  the  windows  :  her  pupils  appear 
very  small,  and  the  iris  large.  Now,  Emily,  turn 
from  the  light,  and  cover  your  eyes  with  your  hand, 
30  as  entirely  to  exclude  it  for  a  few  moments. 

Caroline.  How  very  much  the  pupils  of  her  eyes 
are  now  enlarged,  and  the  iris  diminished.  This  is, 
no  doubt,  the  reason  why  the  eyes  suffer  pain,  when 
from  darkness  they  suddenly  come  into  a  strong  light ; 
for  the  pupil  being  dilated,  a  quantity  of  rays  must 
rush  in  before  it  has  time  to  contract. 

Emily.  And  when  we  go  from  a  strong  light  into 
obscurity,  we  at  first  imagine  ourselves  in  total  dark- 
ness; for  a  sufficient  number  of  rays  cannot  gain  ad- 
mittance into  the  contracted  pupil,  to  enable  us  to  dis- 
tinguish objects  :  but  in  a  few  minutes  it  dilates,  and 
we  clearly  perceive  objects  which  were  before  invi- 
sible. 

Mrs.  B.  It  is  just  so.  The  choroid  c  c,  is  imbued 
with  a  black  liquor,  which  serves  to  absorb  all  the 
rays  that  are  irregularly  reflected,  and  to  convert  the 
body  of  the  eye  into  a  more  perfect  camera  obscura. 
When  the  pupil  is  expanded  to  its  utmost  extent,  it 
is  capable  of  admitting  ten  times  the  quantity  of  light 
that  it  does  when  most  contracted.  In  cats,  and  ani- 
mals which  are  said  to  see  in  the  dark,  the  power  of 
dilatation  and  contraction  of  the  pupil  is  still  greater: 
it  is  computed  that  their  pupils  may  receive  one  hun- 
dred times  more  light  at  one  time  than  at  another. 

Within  these  coverings  of  the  eye-ball  are  contained 
three  transparent  substances,  called  humours.  The 
iirst  occupies  the  space  immediately  behind  the  cornea, 


OF'ilCSJ. 


243 


and  is  called  the  aqueous  humour,//,  from  its  liquidity 
and  its  resemblance  to  water.  Beyond  this  is  situated 
the  crystalline  humour,  g  g^  so  called  from  its  clear- 
ness and  transparency  :  it  has  the  form  of  a  lens,  and 
refracts  the  rays  of  light  in  a  greater  degree  of  per- 
fection than  any  that  have  been  constructed  by  art ; 
it  is  attached  by  two  muscles,  m  7n,  to  each  side  of 
the  choroid.  The  back  part  of  the  eye,  between  the 
crystalline  humour  and  the  retina,  is  filled  by  the  vi- 
treous humour,  h  /i,  which  derives  its  name  from  a 
resemblance  it  is  supposed  to  bear  to  glass  or  vitrified 
substances. 

The  membranous  coverings  of  the  eye  are  intended 
chiefly  for  the  preservation  of  the  retina,  i  «,  which 
is  by  far  the  most  important  part  of  the  eye,  as  it  is 
that  which  receives  the  impression  of  the  objects  of 
sight,  and  conveys  it  to  the  mind.  The  retina  con- 
sists of  an  expansion  of  the  optic  nerve,  of  a  most  per- 
fect whiteness  :  it  proceeds  from  the  brain,  enters 
the  eye,  at  n,  on  the  side  next  the  nose,  and  is  finely 
spread  over  the  interior  surface  of  the  choroid. 

The  rays  of  light  which  enter  the  eye  by  the  pupil 
are  refracted  by  the  several  humours  in  their  passage 
through  them,  and  unite  in  a  focus  on  the  retina. 

Caroline.  I  do  not  understand  the  use  of  these  re- 
fracting humours  :  the  image  of  objects  is  represented 
in  the  camera  obscura,  without  any  such  assistance. 

Mrs.  B.  That  is  true  ;  but  the  representation 
would  be  much  more  strong  and  distinct,  if  we  enlar- 
ged the  opening  of  the  camera  obscura,  and  received 
the  rays  into  it  through  a  lens. 

I  have  told  you  that  rays  proceed  from  bodies  in  all 
possible  directions.  We  must,  therefore,  consider 
every  part  of  an  object  which  sends  rays  to  our  eyes, 
as  points  from  which  the  rays  diverge,  as  from  a  cen- 
tre. 

Emily.  These  divergent  rays,  issuing  from  a  sin- 
gle point,  I  believe  you  told  us,  were  called  a  pencil 
of  rays  ? 

Mrs.  B.   Yes.  Now,  divergent  rays,  on  entering  the 


244 


OPTICS. 


pupil,  do  not  cross  each  other  ;  the  pupil,  however. 
is  sufficiently  large  to  admit  a  small  pencil  of  them  , 
and  these,  if  not  refracted  to  a  focus  by  the  humour^?, 
would  continue  diverging  after  they  had  passed  the 
pupil,  would  fall  dispersed  upon  the  retina,  and  thus 
the  image  of  a  single  point  would  be  expanded  over  a 
large  portion  of  the  retina.  The  divergent  rays  from 
every  other  point  of  the  object  would  be  spread  over 
a  similar  extent  of  space,  and  would  interfere  and  be 
confounded  with  the  first ;  so  that  no  distinct  image 
could  be  formed,  and  the  retina  would  represent  to- 
tal confusion  both  of  figure  and  colour.  Fig.  3.  re- 
presents two  pencils  of  rays  issuing  from  two  points 
of  the  tree  A  B,  and  entering  the  pupil  C,  refracted 
by  the  cryst<illine  humour  D,  and  forming  distinct  ima- 
ges of  the  spot  they  proceed  from,  on  the  retina,  at  a 
h.  Fig.  4.  differs  from  the  preceding,  merely  from 
not  being  supplied  with  a  lens  ;  in  consequence  of 
which  the  pencils  of  rays  are  not  refracted  to  a  focus, 
and  no  distinct  image  is  formed  on  the  retina.  I  have 
delineated  only  the  rays  issuing  from  two  points  of  aa 
object,  and  distinguished  the  two  pencils  in  fig.  4.  by 
describing  one  of  them  with  dotted  lines  :  the  interfe- 
rence of  these  two  pencils  of  rays  on  the  retina  will 
enable  you  to  form  an  idea  of  the  confusion  which 
would  arise,  from  thousands  and  millions  of  points  at 
the  same  instant  pouring  their  divergent  rays  upon 
the  retina. 

Emily.  True  ;  but  I  do  not  yet  well  understand 
how  the  refracting  humours  remedy  this  imperfec- 
tion. 

Mrs.  B.  The  refraction  of  these  several  humours 
unite  the  whole  of  a  pencil  of  rays,  proceeding  from 
any  one  point  of  an  object,  to  a  corresponding  point 
on  the  retina,  and  the  image  is  thus  rendered  distinct 
and  strong.  If  you  conceive,  in  fig.  3.,  every  point 
of  the  tree  to  send  forth  a  pencil  of  rays  similar  to 
those,  A  B,  every  part  of  the  tree  will  be  as  accu- 
rately represented  on  the  retina  as  the  points  ah. 


OPTICS.  245 

Emily.  How  admirably,  how  wonderfully,  this  i* 
contrived  ! 

Caroline.  But  since  the  eye  requires  refracting 
humours  in  order  to  have  a  distinct  representation  form- 
ed on  the  retina,  why  is  not  the  same  refraction  neces- 
sary for  the  image  formed  in  the  camera  obscura  ? 

Mrs.  B.  Because  the  aperture  through  which  we 
received  the  rays  into  the  camera  obscura  is 
extremely  small ;  so  that  but  very  few  of  the  rays  di- 
verging from  a  point  gain  admittance  ;  but  we  will 
now  enlarge  the  aperture,  and  furnish  it  with  a  lens, 
and  you  will  find  the  landscape  to  be  more  perfectly 
represented. 

Caroline.  How  obscure  and  confused  the  image  is 
now  that  you  have  enlarged  the  opening,  without  put- 
ting in  the  lens. 

Mrs.  B.  Such,  or  very  similar,  would  be  the  re- 
presentation on  the  retina,  unassisted  by  the  refract- 
ing humours.  But  see  what  a  difference  is  produced 
by  the  introduction  of  the  lens,  which  collects  each 
pencil  of  divergent  rays  into  their  several  foci. 

Caroline.  The  alteration  is  wonderful :  the  repre- 
sentation is  more  clear,  vivid,  and  beautiful  than 
ever. 

Mrs.  B.  You  will  now  be  able  to  understand  the 
nature  of  that  imperfection  of  sight,  which  arises  from 
the  eyes  being  too  prominent.  In  such  cases,  the 
crystalline  humour,  D,  (fig.  6.)  being  extremely  con- 
vex, refracts  the  rays  too  much,  and  collects  a  pencil, 
proceeding  from  the  object  A  B,  into  a  focus,  F, 
before  they  reach  the  retina.  From  this  focus,  the 
rays  proceed  diverging,  and  consequently  form  a  very 
confused  image  on  the  retina,  at  a  b.  This  is  the  de- 
fect of  short-sighted  people. 

Emily.  I  understand  it  perfectly.  But  why  is  this 
ilefect  remedied  by  bringing  the  object  nearer  to  the 
eye,  as  we  find  to  be  the  case  with  short-sighted  peo- 
ple ? 

Mrs.  B.  The  nearer  you  bring  an  object  to  your 
eye,  the  more  divergent  the  rays  fall  upon  the  crys- 
21* 


246  OPTICS. 

talline  humour,  and  they  are  consequently  not  so  sooy 
converged  to  a  focus  :  this  focus,  therefore,  either 
falls  upon  the  retina,  or  at  least  approaches  nearer  to 
it,  and  the  object  is  proportionally  distinct,  as  in  fig.  6. 

Emily.  The  nearer,  then,  you  bring  an  object  to 
a  lens,  the  further  the  image  recedes  behind  it. 

Mrs.  B.  Certainly.  But  short-sighted  persons 
have  another  resource  for  objects  which  they  cannot 
approach  to  their  eyes  ;  this  is  to  place  a  concave 
lens,  C  D,  (fig.  1.  Plate  XXII.)  before  the  eye,  in 
order  to  increase  the  divergence  of  the  rays.  The 
effect  of  a  concave  lens  is,  you  know,  exactly  the  re- 
verse of  a  convex  one  :  it  renders  parallel  rays  di- 
vergent, and  those  which  are  already  divergent,  still 
more  so.  By  the  assistance  of  such  glasses,  there- 
fore, the  rays  from  a  distant  object  fall  on  the  pupil, 
as  divergent  as  those  from  a  less  distant  object ;  and, 
with  short-sighted  people,  they  throw  the  image  of  a 
distant  object  back  as  far  as  the  retina. 

Caroline.  ^  This  is  an  exceUent  contrivance, 
indeed. 

Mrs.  B.  And  tell  me,  what  remedy  would  you  de- 
vise for  such  persons  as  have  a  contrary  defect  in 
their  sight ;  that  is  to  say,  in  whom  the  crystalline 
humour,  being  too  flat,  does  not  refract  the  rays  sufli- 
ciently,  so  that  they  reach  the  retina  before  they  are 
converged  to  a  point  ? 

Caroline.  I  suppose  that  a  contrary  remedy  must 
be  applied  to  this  defect ;  that  is  to  say,  a  convex 
lens,  L  M,  fig.  2.,  to  make  up  for  the  deficiency  of 
convexity  of  the  crystalline  humour,  O  P.  For  the 
convex  lens  would  bring  the  rays  nearer  together,  so 
that  they  would  fall  either  less  divergent,  or  parallel 
on  the  crystalline  humour  ;  and,  by  being  sooner  con- 
verged to  a  focus,  would  fall  on  the  retina. 

Mrs.  B.  V^ery  well,  Caroline.  This  is  the  rear 
son  why  elderly  people,  the  humours  of  whose  eyes 
are  decayed  by  age,  are  under  the  necessity  of  using 
convex  spectacles.  And  when  deprived  of  that  re- 
source, they  hold  the  object  at  a  distnace  from  their 


FZATE.  jonr. 


OPTICS.  24T 

eyes,  as  in  fig.  4,  in  order  to  bring  the  focus  for- 
warder. 

Caroline.  I  have  often  been  surprised,  when  my 
grandffither  reads  without  his  spectacles,  to  see  him 
hold  the  book  at  a  considerable  distance  from  his  eyes. 
But  I  now  understand  it ;  for  the  more  distant  the  ob- 
ject is  from  the  crystaHine,  the  nearer  the  image  will 
be  to  it. 

Emily.  I  comprehend  the  nature  of  these  two  op- 
posite defects  very  well ;  but  1  cannot  now  conceive 
how  any  sight  can  be  perfect :  for  if  the  crystalline 
humour  is  of  a  proper  degree  of  convexity,  to  bring 
the  image  of  distant  objects  to  a  focus  on  the  retina, 
it  will  not  represent  near  objects  distinctly  ;  and  if,  on 
the  contrary,  it  is  adapted  to  give  a  clear  image  of 
near  objects,  it  will  produce  a  very  imperfect  one  of 
distant  objects. 

Mrs.  B.  Your  observation  is  very  good,  Emily  ; 
and  it  is  tru-e,  that  every  person  would  be  subject  to 
one  of  these  two  defects,  if  we  had  it  not  in  our  power 
to  increase  or  diminish  the  convexity  of  the  crystal- 
line humour,  and  to  project  it  towards,  or  draw  it 
back  from  the  object,  as  circumstances  require.  In 
a  young  well-constructed  eye,  the  two  muscles  to 
which  the  crystalline  humour  is  attached  have  so  per- 
fect a  command  over  it,  that  the  focus  of  the  rays 
constantly  falls  on  the  retina,  and  an  image  is  formed 
equally  distinct  both  of  distant  objects  and  of  those 
which  are  near. 

Caroline.  In  the  eyes  of  fishes,  which  are  the  only 
eyes  I  have  ever  seen  separate  from  the  head,  the 
cornea  does  not  protrude,  in  that  part  of  the  eye 
which  is  exposed  to  view. 

Mrs.  B.  The  cornea  of  the  eye  of  a  fish  is  not 
more  convex  than  the  rest  of  the  ball  of  the  eye  ;  but 
to  supply  this  deficiency,  their  crystalline  humour  is 
spherical,  and  refracts  the  rays  so  much,  that  it  does 
not  require  the  assistance  of  the  cornea  to  bring  them 
to  a  focus  on  the  retina. 

Emily.     Pray  what  is  the  reason  that  we  cannot  seP. 


248  OPTICS. 

an  object  distinctly,  if  we  approach  it  very  near  to 
the  eye  ? 

Mrs.  B.  Because  the  rays  A»ll  on  the  crystalline 
humour  too  divergent  to  be  refracted  to  a  focus  on 
the  retina ;  the  confusion,  therefore,  arising  from 
viewing  an  object  too  near  the  eye,  is  similar  to  that 
which  proceeds  from  a  flattened  crystalline  humour  ; 
the  rays  reach  the  retina  before  they  are  collected  to 
a  focus,  (fig.  4.)  If  it  were  not  for  this  imperfection, 
we  should  be  able  to  see  and  distinguish  the  parts  of 
objects,  which  are  now  invisible  to  us  from  their  mi- 
nuteness ;  for  could  we  approach  ihem  very  near 
the  eye,  their  image  on  the  retina  would  be  so  much 
magnified  as  to  render  them  visible. 

Emily.  And  could  there  be  no  contrivance  to  con- 
vey the  rays  of  objects  viewed  close  to  the  eye,  so 
that  they  should  be  refracted  to  a  focus  on  the  retina  ? 

Mrs.  B.  The  microscope  is  constructed  for  this 
purpose.  The  single  microscope  (fig.  5.)  consists 
simply  of  a  convex  lens,  commonly  called  a  magnify- 
ing glass  ;  in  the  focus  of  which  the  object  is  placed, 
and  through  which  it  is  viewed  :  by  this  means,  you 
are  enabled  to  approach  your  eye  very  near  the  ob- 
ject, for  the  lens  A  B,  by  diminishing  the  divergence 
of  the  rays,  before  they  enter  the  pupil  C,  makes  them 
fall  parallel  on  the  crystalline  humour  D,  by  which 
they  are  refracted  to  a  focus  on  the  retina,  at  R  K. 

Emily.  This  is  a  most  admirable  invention,  and 
nothing  can  be  more  simple,  for  the  lens  magnifies  the 
object  merely  by  allowing  us  to  bring  it  nearer  to 
the  eye. 

Mrs.  B.  Those  lenses,  therefore,  which  have  the 
shortest  focus  will  magnify  the  object  most,  because 
they  enable  us  to  bring  the  object  nearest  to  the  eye. 

Emily.  But  a  lens  that  has  the  shortest  focus  is 
most  bulging  or  convex  ;  and  the  protuberance  of  the 
lens  will  prevent  the  eye  from  approaching  very  near 
to  the  object. 

Mrs.  B.  This  is  remedied  by  making  the  lens  ex- 
tremely small :   it  may  then  be  spherical  without  oc- 


PLATE    XXm 


OPTICS.  249 

cupying  much  space,  and  thus  unite  the  advantages  of 
a  short  focus,  and  of  allowing  the  eye  to  approach  the 
object. 

Caroline.  We  have  a  niicroscope  at  home,  which 
is  a  much  more  complicated  instrument  than  that  you 
have  described. 

Mrs.  B.  It  is  a  double  microscope  (fig.  6.)  in 
which  you  see,  not  the  object  A  B,  but  a  magnified 
image  of  it,  a  b.  In  this  microscope  two  lenses  are 
employed,  the  one,  L  M,  for  the  purpose  of  magnify- 
ing the  object,  is  called  the. object  glass  ;  the  other, 
N  O,  acts  on  the  principle  of  the  single  microscope, 
and  is  called  the  eye-glass. 

There  is  another  kind  of  microscope,  called  the 
solar  microscope,  which  is  the  most  wonderful  from 
its  great  magnifying  power  :  in  this  we  also  view  an 
image  formed  by  a  lens,  not  the  object  itself.  As  the 
sun  shines,  I  can  show  you  the  effect  of  this  micro- 
scope ;  but  for  this  purpose,  we  must  close  the  shut- 
ters, and  admit  only  a  small  portion  of  light,  through 
the  hole  in  the  wiodow-shutter,  which  we  used  for 
the  camera  obscura.  We  shall  now  place  the  ob- 
ject A  B,  (Plate  XXIII.  fig.  1.)  which  is  a  small  in- 
sect, before  the  lens  C  D,  and  nearly  at  its  focas : 
the  image  E  F  will  then  be  represented  on  the  op- 
posite wall  in  the  same  manner  as  the  landscape  was 
in  the  camera  obscura  ;  with  this  difference,  that  it 
will  be  magnified  instead  of  being  diminished.  I  shall 
leave  you  to  account  for  this  by  examining  the  figure. 

Emily.  1  see  it  at  once.  The  image  E  F  is  mag- 
nified, because  it  is  farther  from  the  lens  than  the 
object  A  B  ;  while  the  representation  of  the  land- 
scape was  diminished,  because  it  was  nearer  the  lens 
than  the  landscape  was.  A  lens,  then,  answers  the 
purpose  equally  well,  either  for  magnifying  or  dimi- 
nishing objects  ? 

Mrs.  B.  Yes  :  if  you  wish  to  magnify  the  image, 
you  place  the  object  near  the  focus  of  the  lens  ;  if  you 
wish  to  produce  a  diminished  image,  you  place  the 


250  OPTICS. 

object  at  a  distance  from  the  lens,  in  order  that  the 
image  may  be  formed  in,  or  near  the  focus. 

Carolne.  The  magnifying  power  of  this  micro- 
scope,  is  prodigious ;  but  the  indistinctness  of  the 
image,  for  want  of  light,  is  a  great  imperfection. 
Would  it  not  be  clearer  if  the  opening  in  the  shutter 
were  enlarged  so  as  to  admit  more  light. 

Mrs.  B.  If  the  whole  of  the  light  admitted  does 
not  fall  upon  the  object,  the  effect  will  only  be  to 
make  the  room  lighter,  and  the  image  consequently 
less  distinct. 

Emily.  But  could  you  not  by  means  of  another 
lens  bring  a  large  pencil  of  rays  to  a  focus  on  the  ob- 
ject, and  thus  concentrate  tkt  whole  of  the  light  ad- 
mitted upon  it  ? 

Mrs.  B.  Very  well.  We  shall  enlarge  the  open- 
ing, and  place  the  lens  X  Y  (fig.  2.)  in  it,  to  converge 
the  rays  to  a  focus  on  the  object  A  B.  There  is  but 
one  thing  more  wanting  to  complete  the  solar  micro- 
scope, which  I  shall  leave  to  Caroline's  sagacity  to 
discover. 

Caroline.  Our  microscope  has  a  small  mirror  at- 
tached to  it,  upon  a  moveable  joint,  which  can  be  so 
adjusted  as  to  receive  the  sun's  rays,  and  reflect  them 
upon  the  object  :  if  a  similar  mirror  were  placed  to 
reflect  light  upon  the  lens,  would  it  not  be  a  means 
of  illuminating  the  object  more  perfectly. 

Mrs.  B.  You  are  quite  right.  P  Q  (fig.  2.)  is  a 
small  mirror,  placed  on  the  outside  of  the  window- 
shutter,  which  receives  the  incident  rays  S  S,  and 
reflects  them  on  the  lens  X  Y.  Now  that  we  have 
completed  the  apparatus,  let  us  examine  the  mites  on 
this  piece  of  cheese,  which  I  place  near  the  focus  of 
the  lens. 

Caroline.  Oh,  how  much  more  distinct  the  image 
now  is,  and  how  wonderfully  magnified  !  The  mites 
on  the  cheese  look  like  a  drove  of  pigs  scrambling 
over  rocks. 

Emily.  I  never  saw  any  thing  so  curious.  Now, 
an  immense  piece  of  cheese  has  fallen  :  one  would 


OPTICS.  251 

imagine  it  an  earthquake  :  some  of  the  poor  mites 
must  have  been  crushed  ;  how  fast  they  run, — they 
absolutely  seem  to  gallop. 

But  this  microscope  can  be  used  only  for  transpa- 
rent objects  ;  as  the  light  must  pass  through  them  to 
form  the  image  on  the  wall  ? 

Mrs.  B.  Very  minute  objects,  such  as  are  view- 
ed in  a  microscope,  are  generally  transparent  ;  but 
when  opaque  objects  are  to  be  exhibited,  a  mirror 
M  N  (tig  3.)  is  used  to  reflect  the  light  on  the  side  of 
the  object  next  the  wall  :  the  image  is  then  formed 
by  light  reflected  from  the  object,  instead  of  being 
transmitted  through  it. 

Emily.  Pray,  is  not  a  magic  lanthorn  constructed 
on  the  same  principles  1 

Mrs.  B.  Yes  ;  with  this  difierence,  that  the  light 
is  supplied  by  a  lamp  instead  of  the  sun. 

The  microscope  is  an  excellent  invention,  to  ena- 
ble us  to  see  and  distinguish  objects  which  are  too 
small  to  be  visible  to  the  naked  eye.  But  there  are 
objects  which,  though  not  really  small,  appear  so  to 
us,  from  their  distance  ;  to  these  we  cannot  apply  the 
same  remedy  ;  for  when  a  house  is  so  far  distant  as  to 
be  seen  under  the  same  Hngle  as  a  mite  which  is  close 
to  us,  the  eff*ect  produced  on  the  retina  is  the  same  : 
the  angle  it  subtends  is  not  large  enough  for  it  to 
form  a  distinct  image  on  the  retina. 

Emily.  Since  it  is  impossible,  in  this  case,  to  ap- 
proach the  object  to  the  eye,  cannot  we  by  means  of 
a  lens  bring  an  image  of  it  nearer  to  us  ? 

Mrs.  B.  Yes  ;  but  then,  the  object  being  very 
distant  from  the  focus  of  the  lens,  the  image  would 
be  too  small  to  be  visible  to  tfie  naked  eye. 

Emily.  Then  why  not  look  at  the  image  through 
another  lens,  which  will  act  as  a  microscope,  enable 
us  to  bring  the  image  close  to  the  eye,  and  thus  ren- 
der it  visible  ? 

Mrs.  B.  Very  well,  Emily  ;  I  congratulate  you  on 
having  invented  a  telescope.  In  figure  4,  the  lens 
C  D,  forms  an  image  E  F,  of  the  object  A  B  ;  and  the 


252,  OPTICS. 

lens  X  Y  serves  the  purpose  of  magnifying  that 
image  ;  and  this  is  all  that  is  required  in  a  common  re- 
fracting telescope. 

Emily.  But  in  fig.  4,  the  image  is  not  inverted  on 
the  retina,  as  objects  usually  are  :  it  should  therefore 
appear  to  us  inverted  ;  and  that  is  not  the  case  in  the 
telescopes  I  have  looked  through. 

Mrs.  B.  When  it  is  necessary  to  represent  the 
image  erect,  two  other  lenses  are  required  ;  by  which 
means  a  second  image  is  formed,  the  reverse  of  the 
first,  and  consequently  upright.  These  additional 
glasses  are  used  to  view  terrestrial  objects  ;  for  no 
inconvenience  arises  from  seeing  the  celestial  bodies 
inverted. 

Emily.  The  difference  bctwppn  a  microscope  and 
a  telescope,  seems  to  be  this  ; — a  microscope  produ- 
ces a  magnified  image,  because  the  object  is  nearest 
the  lens  ;  and  a  telescope  produces  a  diminished  im- 
age, because  the  object  is  furthest  from  the  lens. 

Mrs.  B.  Your  observation  applies  only  to  the  lens 
C  D,  or  object-glass,  which  serves  to  bring  an  image 
of  the  object  nearer  the  eye  ^  for  the  lens  X  Y,  or 
eye-glass,  is,  in  fact,  a  microscope,  as  its  purpose  is 
t(D  magnify  the  image. 

When  a  very  great  magnifying  power  is  required, 
telescopes  are  constructed  with  concave  mirrors,  in- 
stead of  lenses.  Concave  mirrors,  you  know,  pro- 
duce, by  redection,  an  effect  similar  to  that  of  convex 
lenses  by  refraction.  In  reflecting  telescopes,  there- 
fore, mirrors  are  used  in  order  to  bring  the  image 
nearer  the  eye  ;  and  a  lens  or  eye-glass  the  same 
as  in  the  refracting  telescope  to  magnify  the  image. 

The  advantage  of  the  reflecting  telescope  is,  that 
mirrors  whose  focus  is  six  feet  will  magnify  as  much 
;is  lenses  of  a  hundred  feet. 

Caroline.  But  I  thought  it  was  the  eye-glass  only 
which  magnified  the  image  ;  and  that  the  other  lens 
served  to  bring  a  diminished  image  nearer  to  the  eye. 

Mrs.  B.  The  image  is  diminished  in  comparison  to 
the  object,  it  is  true  ;  but  it  is  magnified  if  you  com- 


OPTICS.  2J^J 

pare  it  to  the  dimensions  of*  which  it  would  appear 
without  the  intervention  of  any  optical  instrument  ; 
and  this  magnifying  power  is  greater  in  reflecting  than 
in  refracting  telescopes. 

We  must  now  hring  our  observations  to  a  conclu- 
sion, for  I  have  communicated  to  you  tlie  whole  of  my 
very  limited  stock  of  knowledge  of  Natural  Philoso- 
phy. If  it  will  enable  you  to  make  further  progress 
in  that  science,  my  wishes  will  be  sati«tied  ;  biit  re- 
member that,  in  order  that  the  study  of  nature  may  be 
productive  of  happiness,  it  must  lead  to  an  entire  con- 
fidence in  the  wisdom  and  goodness  of  its  bounteous 
Author. 


2JJ 


INDEX. 


Air,  16.  21.  35.  63.  168.  202. 

225. 
Air-pump,  40. 170. 
Angle,  56. 

,  acute,  67. 

,  obtuse,  57. 

of  incidence,  57.   199. 

215. 

of  reflection,  58.   190. 

199.  215. 

of  vision,  209.  210. 


Aphelion,  96. 

Arctic  circle,  115.  125. 

Atmosphere,  129. 160. 168. 180. 

202. 

,  reflection  of,  184. 

,  colour  of,  238. 

,  refraction  of,  223. 

227. 
Attraction,  15.20.30.223. 
,  of  cohesion,  20  43. 

147.  168. 

-,  of  gravitation,  25. 


Barometer,  173. 
Bass,  192. 
Bladder,  170. 
Bodies,  14. 

,  elastic,  51. 62. 

,  luminous,  194. 

,  sonorous,  186. 

,  fall  of,  30.  34.  39.  47. 

,  opaque,  194.  223. 

,  transparent,  194,  223 

Bulk,  22. 


Camera  obscura,  203. 214. 249. 
Capillary  tubes,  24. 
Centre,  61. 

■  of  gravity,  61.  65.  68. 

70.  142. 

of  motion,  61. 69. 142. 

of  magnitude,  61.  67. 


41.90.  102  120.  141.  168. 
Avenue,  209.  210. 
Auditory  Nerve,  191. 
Axis,  99. 

of  motion,  61.  70. 

of  the  earth,  115.  123. 

of  mirrors,  217. 

of  a  lens,  228. 


B 


Balloon,  39. 


Centrifugal  force,  63.  93.  118. 

142. 
Centripetal  force,  63. 93. 
Ceres,  106. 
Circle,  66  117.  119. 
Circular  motion,  60. 93. 
Clouds,  159 
Colours,  30.  229. 
Comets,  107. 
Compression,  53. 
Concord.  192. 
Constellation,  108. 
Convergent  rays,  217. 219. 
Crystals,  17. 
Cylinder,  66. 


256 


INDEX. 


D 

Day,  99.  180. 

Degrees,  56.  117  123.212. 

of  latitude,  118   138. 

of  longitude,  1 18. 138. 

Density,  22. 
Diagonal.  60. 
Diameter,  117. 
Diurnal,  99. 
Discords,  191. 
Divergent  rays,  217. 
Divisibility,  15.  17. 


E 


£artli,25.90. 106. 112.  114 
Echo,  189. 

Eclipse,  135.  139.  197. 
Ecliptic,  109.  116. 
Elastic  bodies,  51.  53. 

fluids,  21.  37.  147.  168. 

Ellipsis,  95. 

Essential  properties,  15. 
Exhalations,  18. 
Extension,  15.  16. 
Equator,  115. 
Equinox,  124.  126. 

-,  precession  of,  132. 


Eye,  203. 


Fal!  of  bodies,  30. 34. 39.  47. 
Figure,  15  17. 
Fluids,  146. 

,  elastic,  147.  168. 

' ,  equilibrium  of,  148. 173. 

,  pressure  of,  149. 163. 1 72. 

Flying,  51. 
Focus,  218. 
of  convex  mirrors,  218. 

of  concave;220. 

. of  a  lens,  228. 

Force,  42. 

centrifugal,  63. 93.  lis. 


Force  of  gravity,  25.  90.  102. 

169. 
Fountains:  167. 
Friction,  87.  167. 
Frigid  zone,  117.  124. 
Fulcrum,  70. 


General  properties  of  bodies, 

14.  15. 
Georgium  Sidus,  107. 
Glass,  227. 

,  refraction  of,  227. 

burning,  232. 

Gold,  154. 

Gravity,  25.  30—41.  43.  47.  64 

65. 

H 

Harmony,  192. 
Heat,  22.  129. 
Hemisphere,  115.  124. 
Hydrometer,  157. 
Hydrostatics,  146. 


Image  on  the  retina,  204.  213 
Image  reversed,  206. 

in  plain  mirror,  214. 

in  convex  ditto,  217. 

in  concave, 217. 


142. 


,  centripetal,  63.93. 
of  projection.  63  92. 


Impenetrability,  15. 
Inclined  plane,  69.84, 
Inertia,  15.  20.  42. 


Juno, 106 
Jupiter,  106.  139. 


Lake,  165. 
Latitude,  US.  138. 
Lens,  228. 

,  convex,  228. 

,  concave,  22S 


LWIXEX. 


357 


Lever,  (59. 

,  first  order,  74. 

,  second  ditto,  76. 

.  third  ditto,  77. 

Light.  195. 

,  jieDcil  of,  195. 

,  rpflrcted,  198. 

of  the  moon,  200. 

,  refraction  of,  220. 

,  absorption  of,  233. 

Liquid,  147. 
Longitude,  118   138. 
Luminous  bodies,  194. 
Lunar  month,  1.34. 
eclipse,  135. 

M 

Machine,  69.  84.  87. 
Mat{ic  lanthorn,  251. 
Mars,  106. 
Matter,  14.  49. 
Mecrhanics,  69. 
Mediums,  195.  223. 
Melody,  193. 
Mercury  planet,  105  140. 
Mercury,  or  quicksilver,  178. 
Meridians,  117. 
Microscope,  248  252. 

,  single,  248. 

,  double,  249. 

. ,  solar,  249. 

Minerals,  17. 
Minutes,  117. 
Monsoons,  183. 
Month,  lunar,  134. 
Momentum,  49.  73 
Moon,101.102. 107. 134.  141. 
Moon-light.  200. 
Motion,  20.  42.  49.  50. 

uniform,  44. 

,  perpetual,  45. 

,  retarded ,  46. 

,  accelerated,  46. 

,  reflected,  55. 

,  compound,  59. 

,  circular,  60.  94. 

,  axis  of,  61 .  70. 

,  centre  of,  61.  69,  142. 

,  diurnal,  99. 


Musical  instruments,  192. 
Mirrors,  214. 

,  reflection  of,  214. 

,  plain  Of  flat,  217. 

,  convex,  217. 

,  concave.  217.  219 

,  axis  of,  217. 

,  burning,  221. 

N 

Neap  tides,  143. 
Nerves,  204. 

,  auditory,  191  20&. 

,  optic,  203.  205, 

,  olfactory,  205. 

Night,  99. 

Nodes,  123.  124, 132, 


Octave,  192. 

Odour,  18. 

Opaque  bodies,  194.  196. 

Optics.  194. 

Orbit,  104. 


Pallas,  106. 

Parabola,  64. 

Parallel  lines,  33. 

Pellucid  bodies,  195, 

Pencil  of  ray?,  196. 

Pendulum,  121. 

Perihelion,  96. 

Perpendicular  lines,  33. 56. 127-. 

Phases,  135. 

Piston,  176. 

Plane,  116. 

Planets,  97.  102.  130. 

Poles,  115 

Polar  star,  124.  138. 

Pond,  165. 

Porosity,  54. 

Power,  mechanical,  69. 

Projection,  63.  92. 

Precession  of  the  equinoxe?, 

132. 
Pulley,  69.  79. 


258 


INDEX. 


Pump,  40.  4i. 

,  sucking,  or  lifting,  176. 

,  forcing,  178.  180. 

Pupil  of  the  eye,  203. 


R 


Rain,  160. 
Rainbow,  232. 
Rarity,  22. 
Ray  of  light,  195. 

of  reflection,  199. 

of  incidence,  199. 

Rays,  intersecting,  203. 
Reaction,  60. 
Receiver,  40. 
Reflection  of  light,  198. 

,  angle  of,  68.  215. 

of  mirrors,  214. 

of  plain  mirrors,  217. 

of  convex    mirrors, 

217. 
i —  of  concave  mirrors, 

217. 
Reflected  motion,  55. 
Refraction,  220. 
of  the   atmosphere, 

227. 


of  glass,  227. 

of  a  lens,  228. 

of  a  prism,  229. 

Resistance,  69. 
Retina,  203. 

,  image  on,  204. 

Rivers,  159. 
Rivulets,  162. 


S 


Satellites,  102.  137.  139. 

Saturn,  106. 

Scales  or  balance,  70. 

Screw,  69.  85. 

Shadow,  136.  196. 

Sidereal  time,  132. 

Sight,  204. 

Signs,  Zodiac,  108.  116. 118. 

Smoke,  19. 38. 

Solar  microscope,  249. 

Solstice,  123.  125. 


Sound,  185. 

, acute,  191. 

,  musical,  192. 

Space,  43. 

Specific  gravity,  152. 

of  air,  173 

Spectrum,  230. 
Speaking  trumpet,  190. 
Sphere,  33.  66.  120. 
Springs,  161. 
Spring  tides,  143. 
Square,  60.  103.  107. 
Stars.  97. 108. 131.138. 
Storms,  181 
Substance,  14, 
Summer,  96.  123. 
Sun,  90.  102  194.226. 
Swimming,  52. 
Syphon,  164. 


Tangent,  63  93. 
Telescope,  251. 
.  — ,  reflecting,  252 

,  refracting.  252. 

Temperate  zone^  117.  126. 
Thermometer,  175. 
Tides,  141. 

,  neap,  143. 

,  spring,  143. 

,  aerial.  185. 

Time,  130.  133. 

,  sidereal.  132. 

,  equal,  133. 

,  solar,  133. 

Tone,  191. 

Torrid  zone,  116.  125.  181. 
Transparent  bodies,  194. 
Treble  and  bass,  192. 
Tropics,  115. 


Valve,  177. 
Vapour,  23.  38.  16(^ 
Velocity,  43.  72. 
Venus,  105,  140. 
Vesta,  106 
Vibration.  ISP. 


INDEX. 


259 


Vihion,  20d. 

,  angle  of,  209. 

,  double,  213. 

U 

Undulations,  188. 
Unison,  192. 

W 

Waters,  147. 

,  spring,  161. 

,  rain,  161. 

,  level  of,  148.  154  159. 

VVed^e,  69  85 

Weit?ht,  22.  30.  120.  152.  169. 

170. 
Wheel  aad  a&le,  69.  83. 


Wind,  180. 

,  trade,  182. 

,  periodical,  183. 

Winch,  86. 
Winter,  96.  125. 


Year,  180. 

,  sidf-real,  132 

,  solar,  133. 


Zodiac,  108.  118. 
Zone,  116. 

,  torrid,  116. 125. 181 .  226 

,  temperate,  117. 125. 

,  frigid,  117.  124. 


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